% COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) flclear fem % COMSOL version clear vrsn vrsn.name = 'COMSOL 3.5'; vrsn.ext = ''; vrsn.major = 0; vrsn.build = 494; vrsn.rcs = '$Name: $'; vrsn.date = '$Date: 2008/09/19 16:09:48 $'; fem.version = vrsn; % Geometry g1=block3('0.0005','0.004536','0.000017','base','corner','pos',{'0','0','0'},'axis',{'0','0','1'},'rot','0'); g2=block3('0.0005','0.004502','0.00025','base','corner','pos',{'0','0.000017','0.000017'},'axis',{'0','0','1'},'rot','0'); g3=block3('0.0005','0.000434','0.000045','base','corner','pos',{'0','0','0'},'axis',{'0','0','1'},'rot','0'); g3=move(g3,[0,0.000017,0.000267]); g4=block3('0.0005','0.0012','0.000045','base','corner','pos',{'0','0.000451','0.000267'},'axis',{'0','0','1'},'rot','0'); g5=block3('0.0005','0.000434','0.000045','base','corner','pos',{'0','0.001651','0.000267'},'axis',{'0','0','1'},'rot','0'); g6=block3('0.0005','0.000366','0.000047','base','corner','pos',{'0','0.002085','0.000267'},'axis',{'0','0','1'},'rot','0'); g7=block3('0.0005','0.000434','0.000267','base','corner','pos',{'0','0.002451','0.000267'},'axis',{'0','0','1'},'rot','0'); g8=block3('0.0005','0.000434','0.000045','base','corner','pos',{'0','0.002451','0.000267'},'axis',{'0','0','1'},'rot','0'); g9=block3('0.0005','0.0012','0.000045','base','corner','pos',{'0','0.002885','0.000267'},'axis',{'0','0','1'},'rot','0'); g10=block3('0.0005','0.000434','0.000045','base','corner','pos',{'0','0.004085','0.000267'},'axis',{'0','0','1'},'rot','0'); g11=block3('0.0005','0.000017','0.000579','base','corner','pos',{'0','0','0'},'axis',{'0','0','1'},'rot','0'); g12=block3('0.0005','0.000017','0.000579','base','corner','pos',{'0','0.004519','0'},'axis',{'0','0','1'},'rot','0'); g13=block3('0.0005','0.004502','0.000250','base','corner','pos',{'0','0','0.000312'},'axis',{'0','0','1'},'rot','0'); g13=move(g13,[0,0.000017,0]); g14=block3('0.0005','0.004536','0.000250','base','corner','pos',{'0','0','0'},'axis',{'0','0','1'},'rot','0'); g14=move(g14,[0,0,0.000312]); % Geometry objects clear s s.objs={g1,g2,g3,g4,g5,g6,g8,g9,g10,g11,g12,g14}; s.name={'BLK1','BLK2','E_Wall','Air0','MicroStrip1','Air1', ... 'MicroStrip2','Air2','E_Wall2','BLK3','E_Wall_ln2','BLK4'}; s.tags={'g1','g2','g3','g4','g5','g6','g8','g9','g10','g11','g12', ... 'g14'}; fem.draw=struct('s',s); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry g13=block3('0.0005','0.004505','0.00025','base','corner','pos',{'0','0.000017','0.000312'},'axis',{'0','0','1'},'rot','0'); g15=block3('0.0005','0.000451','0.000045','base','corner','pos',{'0','0','0'},'axis',{'0','0','1'},'rot','0'); g15=move(g15,[0,0,0.000267]); g16=block3('0.0005','0.000366','0.000045','base','corner','pos',{'0','0.002085','0.000312'},'axis',{'0','0','1'},'rot','0'); g16=move(g16,[0,0,-0.000045]); g17=block3('0.0005','0.000451','0.000045','base','corner','pos',{'0','0.004085','0.000267'},'axis',{'0','0','1'},'rot','0'); garr=split(g15); [g18]=deal(garr{:}); g19=block3('0.0005','0.000017','0.000579','base','corner','pos',{'0','0','0'},'axis',{'0','0','1'},'rot','0'); g20=block3('0.0005','0.004536','0.000017','base','corner','pos',{'0','0','0.000562'},'axis',{'0','0','1'},'rot','0'); g21=block3('0.0005','0.000017','0.000579','base','corner','pos',{'0','0.004519','0'},'axis',{'0','0','1'},'rot','0'); % Geometry objects clear s s.objs={g9,g8,g2,g1,g5,g4,g13,g16,g17,g18,g19,g20,g21}; s.name={'Air2','MicroStrip2','Rogers','E_Wall_base','MicroStrip1', ... 'Air0','Air_UP','Air1','E_Wall2_sd','E_Wall1_sd','E_wall_ln1', ... 'E_Wall_UP','E_Wall_ln2'}; s.tags={'g9','g8','g2','g1','g5','g4','g13','g16','g17','g18','g19', ... 'g20','g21'}; fem.draw=struct('s',s); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry g3=block3('0.0005','0.004502','0.00025','base','corner','pos',{'0','0.000017','0.000562'},'axis',{'0','0','1'},'rot','0'); g3=move(g3,[0,0,-0.000250]); % Analyzed geometry clear s s.objs={g9,g21,g8,g20,g16,g17,g18,g19,g2,g1,g5,g4,g3}; s.name={'Air2','E_Wall_ln2','MicroStrip2','E_Wall_UP','Air1', ... 'E_Wall2_sd','E_Wall1_sd','E_wall_ln1','Rogers','E_Wall_base', ... 'MicroStrip1','Air0','Air_UP'}; s.tags={'g9','g21','g8','g20','g16','g17','g18','g19','g2','g1','g5', ... 'g4','g3'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5, ... 'hpnt',20, ... 'xscale',1.0, ... 'yscale',1.0, ... 'zscale',1.0, ... 'jiggle','on', ... 'methodfac','tri'); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','numeric','numeric','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = 'TE'; bnd.name = ''; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','field','field','energy','energy'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,5,2,2,3,2,2,3,2, ... 2,1,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,5,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,6,4,4,6,4,6,4,6,6,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,0}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,3,3,1,3,1,3,1,3,3,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.type = 'cont'; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,5,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,5,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,2,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat4_mur',1,1,'mat4_mur'}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat4_sigma',0,0,'mat4_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat4_epsilonr',3,1,'mat4_epsilonr'}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,7,7,5,7,8,7,8,7,7,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Solve problem fem.sol=femeig(fem, ... 'u',0, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'texeyez10','texeyez21','texeyez20','en'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tex2ey2ez210','tExEyEz21'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'neigs',3, ... 'shift',-43.383992*i, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'eigname','lambda', ... 'eigref','0', ... 'linsolver','umfpack', ... 'thresh',0.1, ... 'umfalloc',0.7, ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','neff_rfwb(1)=1.431404 (1) Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023215272901501514,0.0010644410874289432,-1.1191045594671467E-4], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0.017428488520812163,-9.133883796357411E-4,0.9998476951563913], ... 'camva',5.989927771173074, ... 'camprojection','orthographic', ... 'transparency',1.0); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','numeric','numeric','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = 'TE'; bnd.name = ''; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','field','field','energy','energy'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,5,2,2,3,2,2,3,2, ... 2,1,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,5,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,6,4,4,6,4,6,4,6,6,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,0}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,3,3,1,3,1,3,1,3,3,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.type = 'cont'; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,5,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,5,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,2,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat4_mur',1,1,'mat4_mur'}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat4_sigma',0,0,'mat4_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat4_epsilonr',3,1,'mat4_epsilonr'}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,7,7,5,7,8,7,8,7,7,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Mapping current solution to extended mesh init = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tex2ey2ez210','tExEyEz21'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023215272901501514,0.0010644410874289432,-1.1191045594671467E-4], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0.017428488520812163,-9.133883796357411E-4,0.9998476951563913], ... 'camva',5.989927771173065, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','numeric','numeric','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = 'TE'; bnd.name = ''; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','field','field','energy','energy'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,5,2,2,3,2,2,3,2, ... 2,1,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,5,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,6,4,4,6,4,6,4,6,6,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,0}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,3,3,1,3,1,3,1,3,3,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.type = 'cont'; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,5,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,5,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,2,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat4_mur',1,1,'mat4_mur'}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat4_sigma',0,0,'mat4_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat4_epsilonr',3,1,'mat4_epsilonr'}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,7,7,5,7,8,7,8,7,7,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Solve problem fem.sol=femeig(fem, ... 'u',fem0.sol, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'texeyez10','texeyez21','texeyez20','en'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tExEyEz21','tex2ey2ez210'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'neigs',3, ... 'shift',2.07, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'eigname','lambda', ... 'eigref','0', ... 'linsolver','umfpack', ... 'thresh',0.1, ... 'umfalloc',0.7, ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ex','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, x component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ez','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, z component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'normE_rfw','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, norm [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Total energy density, time average [J/m^3] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.75669899507536, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Weav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric energy density, time average [J/m^3] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.75669899507536, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Dy_rfw','cont','internal','recover','off','unit','C/m^2'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric displacement, y component [C/m^2] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.75669899507536, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','flat', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','interp', ... 'slicefacestyle','none', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','hot(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','grayprint(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum',1, ... 'phase',0, ... 'title','lambda(1)=6.078179e-7 Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[1.250000059371814E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.756698995075359, ... 'camprojection','orthographic', ... 'transparency',1.0); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','numeric','numeric','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = 'TE'; bnd.name = ''; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','field','field','energy','energy'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,5,2,2,3,2,2,3,2, ... 2,1,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,5,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,6,4,4,6,4,6,4,6,6,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,0}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,3,1,3,1,3,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat4_mur',1,1,'mat4_mur'}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat4_sigma',0,0,'mat4_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat4_epsilonr',3,1,'mat4_epsilonr'}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,7,8,7,8,7,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tex2ey2ez210','tExEyEz21'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.011273896531200055,-0.014500878796957543,0.011096631133616867], ... 'camtarget',[0.0010694269814653162,0.0015852535899354198,-6.097957409246637E-4], ... 'camup',[0,0,1], ... 'camva',2.4622478812948794, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % Plot solution postplot(fem, ... 'slicedata',{'normE_rfw','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, norm [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002347075454959116,1.5770763457841264E-4], ... 'camtarget',[1.250000059371814E-4,0.002347075454959116,1.5770763457841264E-4], ... 'camup',[0,0,1], ... 'camva',6.798481457448295, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002347075454959116,1.5770763457841264E-4], ... 'camtarget',[1.250000059371814E-4,0.002347075454959116,1.5770763457841264E-4], ... 'camup',[0,0,1], ... 'camva',6.798481457448295, ... 'camprojection','orthographic', ... 'transparency',1.0); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','numeric','numeric','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = 'TE'; bnd.name = ''; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','field','field','energy','energy'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,5,2,2,3,2,2,3,2, ... 2,1,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,5,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,6,4,4,6,4,6,4,6,6,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,0}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,3,1,3,1,3,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat4_mur',1,1,'mat4_mur'}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat4_sigma',0,0,'mat4_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat4_epsilonr',3,1,'mat4_epsilonr'}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,7,8,7,8,7,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tExEyEz21','tex2ey2ez210'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023023164625632895,0.002347075454959116,1.5770763457841264E-4], ... 'camtarget',[1.250000059371814E-4,0.002347075454959116,1.5770763457841264E-4], ... 'camup',[0,0,1], ... 'camva',6.798481457448296, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','numeric','numeric','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = 'TE'; bnd.name = ''; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','energy','energy','field','field'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,3,2,2,3,2,2,3,2, ... 2,1,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,3,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,6,4,6,4,4,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,0}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,3,1,3,1,3,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat4_mur',1,1,'mat4_mur'}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat4_sigma',0,0,'mat4_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat4_epsilonr',3,1,'mat4_epsilonr'}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,7,8,7,8,7,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tex2ey2ez210','tExEyEz21'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'isodata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'isolevels',5, ... 'isoedgestyle','none', ... 'isofacestyle','interp', ... 'isobar','on', ... 'isocolorbar','on', ... 'isomap','jet(1024)', ... 'isomapstyle','auto', ... 'isostriptol',0.01, ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m] Isosurface: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.011875819895401462,-0.013534676129461517,0.011789646115445645], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.86608781117711, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.011875819895401462,-0.013534676129461517,0.011789646115445645], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.866087811177054, ... 'camprojection','orthographic', ... 'transparency',1.0); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0},{0;0;0},{1;0;0},{0;0;0},{1; ... 0;0},{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','userdef','numeric','userdef','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = {'TE','TE','TEM','TE','TEM','TEM'}; bnd.name = {'PEC','Kont','Port1_face','Port2_face','Port1_T','Port2_T'}; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','energy','energy','field','field'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,3,2,2,3,2,2,3,2, ... 2,1,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,3,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,6,4,6,4,4,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,'mat6_sigma'}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,3,1,3,1,3,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat3_mur',1,1}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat3_sigma',0,'mat5_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat3_epsilonr',3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,7,5,7,5,7,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.mat{5}.name='Air_1'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{5}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{5}.variables.gamma='1.4'; lib.mat{5}.variables.sigma='0[S/m]'; lib.mat{5}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{5}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{5}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{5}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{5}.functions = fcns; lib.mat{6}.name='Air_2'; lib.mat{6}.varname='mat6'; lib.mat{6}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{6}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{6}.variables.gamma='1.4'; lib.mat{6}.variables.sigma='0[S/m]'; lib.mat{6}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{6}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{6}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{6}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{6}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tExEyEz21','tex2ey2ez210'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.012357177726020458,-0.013155583079877079,0.011803022148590444], ... 'camtarget',[-2.3135781874464444E-4,0.002647093089787769,3.0287602564951484E-4], ... 'camup',[0,0,1], ... 'camva',6.8660878111771755, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % Plot solution postplot(fem, ... 'slicedata',{'Wav_rfw','cont','internal','recover','off','unit','J/m^3'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Total energy density, time average [J/m^3]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.02644701517075834,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',5.651530424948445, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Poyav_rfw','cont','internal','recover','off','unit','W/m^2'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Power flow, time average, y component [W/m^2]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.02644701517075834,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',5.651530424948442, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'normE_rfw','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, norm [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.02644701517075834,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',5.651530424948442, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.02644701517075834,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',5.651530424948442, ... 'camprojection','orthographic', ... 'transparency',1.0); % Plot solution postplot(fem, ... 'slicedata',{'normE_rfw','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, norm [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.02644701517075834,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',5.651530424948442, ... 'camprojection','orthographic', ... 'transparency',1.0); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0},{0;0;0},{1;0;0},{0;0;0},{1; ... 1;1},{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','userdef','numeric','userdef','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = {'TE','TE','TEM','TE','TEM','TEM'}; bnd.name = {'PEC','Kont','Port1_face','Port2_face','Port1_T','Port2_T'}; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','energy','energy','field','field'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,3,2,2,3,2,2,3,2, ... 2,1,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,3,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,6,4,6,4,4,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,'mat6_sigma'}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,3,1,3,1,3,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat3_mur',1,1}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat3_sigma',0,'mat5_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat3_epsilonr',3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,7,5,7,5,7,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.mat{5}.name='Air_1'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{5}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{5}.variables.gamma='1.4'; lib.mat{5}.variables.sigma='0[S/m]'; lib.mat{5}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{5}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{5}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{5}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{5}.functions = fcns; lib.mat{6}.name='Air_2'; lib.mat{6}.varname='mat6'; lib.mat{6}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{6}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{6}.variables.gamma='1.4'; lib.mat{6}.variables.sigma='0[S/m]'; lib.mat{6}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{6}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{6}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{6}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{6}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tex2ey2ez210','tExEyEz21'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'normE_rfw','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, norm [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.013561141365326098,-0.01573102983046134,0.013388007571946704], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',7.565379412712406, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.013561141365326098,-0.01573102983046134,0.013388007571946704], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',7.565379412712396, ... 'camprojection','orthographic', ... 'transparency',1.0); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0},{0;0;0},{1;0;0},{0;0;0},{1; ... 0;1},{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','userdef','numeric','userdef','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = {'TE','TE','TEM','TE','TEM','TEM'}; bnd.name = {'PEC','Kont','Port1_face','Port2_face','Port1_T','Port2_T'}; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','energy','energy','field','field'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,3,2,2,3,2,2,3,2, ... 2,1,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,3,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,6,4,6,4,4,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,'mat6_sigma'}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,3,1,3,1,3,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat3_mur',1,1}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat3_sigma',0,'mat5_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat3_epsilonr',3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,7,5,7,5,7,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.mat{5}.name='Air_1'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{5}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{5}.variables.gamma='1.4'; lib.mat{5}.variables.sigma='0[S/m]'; lib.mat{5}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{5}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{5}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{5}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{5}.functions = fcns; lib.mat{6}.name='Air_2'; lib.mat{6}.varname='mat6'; lib.mat{6}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{6}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{6}.variables.gamma='1.4'; lib.mat{6}.variables.sigma='0[S/m]'; lib.mat{6}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{6}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{6}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{6}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{6}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tExEyEz21','tex2ey2ez210'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.013811252210603035,-0.015494308412302702,0.013449574863295089], ... 'camtarget',[-1.1083340257599106E-7,0.00250472145836197,3.5106728385310117E-4], ... 'camup',[0,0,1], ... 'camva',7.565379412712645, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % Integrate I1=postint(fem,'Wav_rfw', ... 'unit','J', ... 'recover','off', ... 'dl',[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21], ... 'edim',3, ... 'intorder',4, ... 'geomnum',1, ... 'complexfun','on', ... 'matherr','off', ... 'solnum','end', ... 'phase',0); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.011875819895401462,-0.013534676129461517,0.011789646115445645], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.866087811177054, ... 'camprojection','orthographic', ... 'transparency',1.0); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {0,0,1,0,1,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'E0','cont','port','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'auto','auto','TEM','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0},{0;0;0},{0;0;0},{0;0;0},{1; ... 0;1},{0;0;0}}; bnd.applmode = {0,0,'rfwb','rfwb2','rfwb','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','userdef','numeric','userdef','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = {'TE','TE','TEM','TE','TEM','TEM'}; bnd.name = {'PEC','Kont','Port1_face','Port2_face','Port1_T','Port2_T'}; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'field','field','energy','energy','field','field'}; bnd.portnr = {1,1,1,2,1,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [3,1,1,3,1,2,3,1,2,3,1,2,3,1,2,1,3,2,1,3,2,2,3,2,2,3,2,2,3,2, ... 2,1,3,2,2,2,5,2,2,2,3,2,2,2,5,2,2,2,3,2,2,2,3,2,2,2,3,2,1,3,2,2,3,2,2, ... 3,2,2,3,2,2,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,6,4,6,4,4,4,4,4,4,4]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,'mat6_sigma'}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,3,1,3,1,3,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat3_mur',1,1}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat3_sigma',0,'mat5_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat3_epsilonr',3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,7,5,7,5,7,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.mat{5}.name='Air_1'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{5}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{5}.variables.gamma='1.4'; lib.mat{5}.variables.sigma='0[S/m]'; lib.mat{5}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{5}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{5}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{5}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{5}.functions = fcns; lib.mat{6}.name='Air_2'; lib.mat{6}.varname='mat6'; lib.mat{6}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{6}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{6}.variables.gamma='1.4'; lib.mat{6}.variables.sigma='0[S/m]'; lib.mat{6}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{6}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{6}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{6}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{6}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tex2ey2ez210','tExEyEz21'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.011875819895401462,-0.013534676129461517,0.011789646115445645], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.866087811177229, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry g6=block3('5.0E-4','0.004536','1.7E-5','base','corner','pos',{'0','0','7.62E-4'},'axis',{'0','0','1'},'rot','0'); g7=block3('5.0E-4','1.7E-5','7.79E-4','base','corner','pos',{'0','0','0'},'axis',{'0','0','1'},'rot','0'); g10=block3('5.0E-4','0.004502','4.5E-4','base','corner','pos',{'0','1.7E-5','3.12E-4'},'axis',{'0','0','1'},'rot','0'); g11=block3('5.0E-4','1.7E-5','7.79E-4','base','corner','pos',{'0','0.004519','0'},'axis',{'0','0','1'},'rot','0'); % Analyzed geometry clear s s.objs={g9,g8,g16,g17,g18,g2,g1,g5,g4,g6,g7,g10,g11}; s.name={'Air2','MicroStrip2','Air1','E_Wall2_sd','E_Wall1_sd', ... 'Rogers','E_Wall_base','MicroStrip1','Air0','E_Wall_UP','E_wall_ln1', ... 'Air_UP','E_Wall_ln2'}; s.tags={'g9','g8','g16','g17','g18','g2','g1','g5','g4','g6','g7', ... 'g10','g11'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5, ... 'hpnt',20, ... 'xscale',1.0, ... 'yscale',1.0, ... 'zscale',1.0, ... 'jiggle','on', ... 'methodfac','tri'); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {1,0,0,1,0,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'port','E0','cont','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'TEM','auto','auto','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0},{0;0;0},{0;0;0},{1;0;1},{0; ... 0;0},{0;0;0}}; bnd.applmode = {'rfwb',0,0,'rfwb','rfwb2','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','userdef','userdef','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = {'TEM','TE','TE','TEM','TE','TEM'}; bnd.name = {'Port1_face','PEC','Kont','Port1_T','Port2_face','Port2_T'}; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'energy','field','field','field','energy','field'}; bnd.portnr = {1,1,1,1,2,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,5,5,5,5,5,6,5,6,5,5,5,5,5,5,5]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,'mat6_sigma'}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'','','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,3,1,3,1,3,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,5,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1, ... 2,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1, ... 1,1,1,1,1,1,1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat3_mur',1,1}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','epsr'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat3_sigma',0,'mat5_sigma'}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat3_epsilonr',3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,1,3,3,3,4,3,3,3,1,3,3,3,4,3,3,3,1,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3, ... 1,3,3,1,3,3,2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,7,5,7,5,7,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... 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'273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.mat{5}.name='Air_1'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{5}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{5}.variables.gamma='1.4'; lib.mat{5}.variables.sigma='0[S/m]'; lib.mat{5}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{5}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{5}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{5}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{5}.functions = fcns; lib.mat{6}.name='Air_2'; lib.mat{6}.varname='mat6'; lib.mat{6}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{6}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{6}.variables.gamma='1.4'; lib.mat{6}.variables.sigma='0[S/m]'; lib.mat{6}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{6}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{6}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{6}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{6}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tex2ey2ez210','tExEyEz21'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.02325029225775622,0.002268000040203333,2.894999925047159E-4], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,2.894999925047159E-4], ... 'camup',[0,0,1], ... 'camva',6.034881903608189, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry g3=block3('5e-4','0.004502','4.5e-4','base','corner','pos',{'0','1.7e-5','2.67e-4'},'axis',{'0','0','1'},'rot','0'); g12=block3('5.0E-4','0.004502','4.95E-4','base','corner','pos',{'0','1.7E-5','2.67E-4'},'axis',{'0','0','1'},'rot','0'); % Analyzed geometry clear s s.objs={g7,g11,g8,g17,g18,g2,g1,g6,g5,g12}; s.name={'E_wall_ln1','E_Wall_ln2','MicroStrip2','E_Wall2_sd', ... 'E_Wall1_sd','Rogers','E_Wall_base','E_Wall_UP','MicroStrip1','BLK1'}; s.tags={'g7','g11','g8','g17','g18','g2','g1','g6','g5','g12'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5, ... 'hpnt',20, ... 'xscale',1.0, ... 'yscale',1.0, ... 'zscale',1.0, ... 'jiggle','on', ... 'methodfac','tri'); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1,2,1,2, ... 1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1, ... 1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {1,0,0,1,0,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'port','E0','cont','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'TEM','auto','auto','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0},{0;0;0},{0;0;0},{1;0;1},{0; ... 0;0},{0;0;0}}; bnd.applmode = {'rfwb',0,0,'rfwb','rfwb2','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','userdef','userdef','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = {'TEM','TE','TE','TEM','TE','TEM'}; bnd.name = {'Port1_face','PEC','Kont','Port1_T','Port2_face','Port2_T'}; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'energy','field','field','field','energy','field'}; bnd.portnr = {1,1,1,1,2,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,3,3,4,3,3,3,3,3,4,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,5,5,5,5,5,5,5,5,5,5,6,6,5,5,5,5,5,5]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,'mat6_sigma'}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'M','R','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,1,1,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,3,3,1,3,3,3,3,3,1,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,3,3,3,3,3,3,3,3,5,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1,2,1,2, ... 1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1, ... 1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat3_mur',1,1}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat3_sigma',0,0}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat3_epsilonr',3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,7,3,3,1,3, ... 3,2,3,3,4,3,3,3,3,3,4,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,5,5,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.mat{5}.name='Air_1'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{5}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{5}.variables.gamma='1.4'; lib.mat{5}.variables.sigma='0[S/m]'; lib.mat{5}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{5}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{5}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{5}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{5}.functions = fcns; lib.mat{6}.name='Air_2'; lib.mat{6}.varname='mat6'; lib.mat{6}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{6}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{6}.variables.gamma='1.4'; lib.mat{6}.variables.sigma='0[S/m]'; lib.mat{6}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{6}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{6}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{6}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{6}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tExEyEz21','tex2ey2ez210'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.013010019166551288,-0.012776354618983129,0.012030043357230421], ... 'camtarget',[-8.066286339464431E-4,0.003127413557797647,4.5632913473390367E-4], ... 'camup',[0,0,1], ... 'camva',7.30303395797841, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','longest', ... 'subdomain',[9]); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','longest', ... 'subdomain',[9]); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5, ... 'hpnt',20, ... 'xscale',1.0, ... 'yscale',1.0, ... 'zscale',1.0, ... 'jiggle','on', ... 'methodfac','tri'); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','longest', ... 'subdomain',[9]); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','longest', ... 'subdomain',[9]); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','longest', ... 'subdomain',[9]); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5, ... 'hpnt',20, ... 'xscale',1.0, ... 'yscale',1.0, ... 'zscale',1.0, ... 'jiggle','on', ... 'methodfac','tri'); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1,2,1,2, ... 1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1, ... 1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {1,0,0,1,0,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'port','E0','cont','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'TEM','auto','auto','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0},{0;0;0},{0;0;0},{1;0;1},{0; ... 0;0},{0;0;0}}; bnd.applmode = {'rfwb',0,0,'rfwb','rfwb2','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','userdef','userdef','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = {'TEM','TE','TE','TEM','TE','TEM'}; bnd.name = {'Port1_face','PEC','Kont','Port1_T','Port2_face','Port2_T'}; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'energy','field','field','field','energy','field'}; bnd.portnr = {1,1,1,1,2,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,3,3,4,3,3,3,3,3,4,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,5,5,5,5,5,5,5,5,5,5,6,6,5,5,5,5,5,5]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,'mat6_sigma'}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'M','R','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,1,1,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,3,3,1,3,3,3,3,3,1,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,3,3,3,3,3,3,3,3,5,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1,2,1,2, ... 1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1, ... 1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat3_mur',1,1}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat3_sigma',0,0}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat3_epsilonr',3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,7,3,3,1,3, ... 3,2,3,3,4,3,3,3,3,3,4,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,5,5,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... 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'273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.mat{5}.name='Air_1'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{5}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{5}.variables.gamma='1.4'; lib.mat{5}.variables.sigma='0[S/m]'; lib.mat{5}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{5}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{5}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{5}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{5}.functions = fcns; lib.mat{6}.name='Air_2'; lib.mat{6}.varname='mat6'; lib.mat{6}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{6}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{6}.variables.gamma='1.4'; lib.mat{6}.variables.sigma='0[S/m]'; lib.mat{6}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{6}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{6}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{6}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{6}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tExEyEz21','tex2ey2ez210'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[0.023397428456867396,0.002268000040203333,3.8949999725446105E-4], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,3.8949999725446105E-4], ... 'camup',[0,0,1], ... 'camva',5.996591505953203, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % Integrate I1=postint(fem,'nPoav_rfw', ... 'unit','W', ... 'recover','off', ... 'dl',[1,4,7,10,13,17,20,23,26,29,47,51,54,57,60,63], ... 'edim',2, ... 'intorder',4, ... 'geomnum',1, ... 'complexfun','on', ... 'matherr','off', ... 'solnum','end', ... 'phase',0); % Integrate I2=postint(fem,'nPoav_rfw', ... 'unit','W', ... 'recover','off', ... 'dl',[1,4,7,10,13,17,20,23,26,29,47,51,54,57,60,63], ... 'edim',2, ... 'intorder',4, ... 'geomnum',1, ... 'complexfun','on', ... 'matherr','off', ... 'solnum','end', ... 'phase',0); % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1,2,1,2, ... 1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1, ... 1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {1,0,0,1,0,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'port','E0','cont','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'TEM','auto','auto','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0},{0;0;0},{0;0;0},{1;0;1},{0; ... 0;0},{0;0;0}}; bnd.applmode = {'rfwb',0,0,'rfwb','rfwb2','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','userdef','userdef','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = {'TEM','TE','TE','TEM','TE','TEM'}; bnd.name = {'Port1_face','PEC','Kont','Port1_T','Port2_face','Port2_T'}; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'energy','field','field','field','energy','field'}; bnd.portnr = {1,1,1,1,2,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,3,3,4,3,3,3,3,3,4,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,5,5,5,5,5,5,5,5,5,5,6,6,5,5,5,5,5,5]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,'mat6_sigma'}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'M','R','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,1,1,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,3,3,1,3,3,3,3,3,1,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,3,3,3,3,3,3,3,3,5,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1,2,1,2, ... 1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1, ... 1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat3_mur',1,1}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat3_sigma',0,0}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat3_epsilonr',3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,7,3,3,1,3, ... 3,2,3,3,4,3,3,3,3,3,4,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,5,5,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.mat{5}.name='Air_1'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{5}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{5}.variables.gamma='1.4'; lib.mat{5}.variables.sigma='0[S/m]'; lib.mat{5}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{5}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{5}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{5}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{5}.functions = fcns; lib.mat{6}.name='Air_2'; lib.mat{6}.varname='mat6'; lib.mat{6}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{6}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{6}.variables.gamma='1.4'; lib.mat{6}.variables.sigma='0[S/m]'; lib.mat{6}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{6}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{6}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{6}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{6}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tex2ey2ez210','tExEyEz21'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.011953390520730477,-0.013635768136577449,0.011963214219750978], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,3.8949999725446105E-4], ... 'camup',[0,0,1], ... 'camva',7.303033957978423, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on'); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Application mode 1 clear appl appl.mode.class = 'ElectromagneticWaves'; appl.mode.type = 'cartesian'; appl.dim = {'Ex','Ey','Ez','Hx','Hy','Hz','Ax','Ay','Az','scEx','scEy', ... 'scEz','scHx','scHy','scHz','psi'}; appl.sdim = {'x','y','z'}; appl.name = 'rfw'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''Ex'',''Ey'',''Ez''})','shlag(2,''psi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfw'; clear prop prop.elemdefault='Vec2'; prop.analysis='harmonic'; prop.solvefor='E'; prop.inputvar='nu'; prop.eigtype='freq'; prop.divcond='off'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'tlmx','tlmy','tlmz'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.pnt = pnt; clear edg edg.Im0 = 0; edg.I0 = 0; edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,2,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,1,2,1,2, ... 1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1, ... 1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.inport = {1,0,0,1,0,0}; bnd.eta = 1; bnd.murbnd = 1; bnd.kdir = {{'-nx_rfw';'-ny_rfw';'-nz_rfw'}}; bnd.hport = 1; bnd.I0 = 0; bnd.srcpnt = {{0;0;0}}; bnd.mbsource = 'E'; bnd.Z_ref = 50.0; bnd.type = {'port','E0','cont','port','port','port'}; bnd.Js0 = {{0;0;0}}; bnd.farfield = {{}}; bnd.nummodetype = {'TEM','auto','auto','TEM','TEM','TEM'}; bnd.E0 = {{0;0;0},{0;0;0},{0;0;0},{1;0;1},{0; ... 0;0},{0;0;0}}; bnd.applmode = {'rfwb',0,0,'rfwb','rfwb2','rfwb2'}; bnd.nucutoff = 0; bnd.A0 = {{0;0;0}}; bnd.index = 0; bnd.kper = {{0;0;0}}; bnd.V0 = 1; bnd.rectmodetype = 'TE'; bnd.modenum = '10'; bnd.scsource = 'E'; bnd.lporttype = 'uniform'; bnd.nu0 = 0; bnd.matparams = 'epsr'; bnd.modespec = {'userdef','userdef','userdef','userdef','numeric','numeric'}; bnd.epsilonrbnd = 1; bnd.srcaxis = {{0;0;1}}; bnd.circmodenum = '11'; bnd.chsrcdst = 0; bnd.Pport = 1; bnd.pertype = 'sym'; bnd.symmetryz = 0; bnd.beta = 0; bnd.wport = 1; bnd.symmetryx = 0; bnd.symmetryy = 0; bnd.Es = {{0;0;0}}; bnd.usermodetype = {'TEM','TE','TE','TEM','TE','TEM'}; bnd.name = {'Port1_face','PEC','Kont','Port1_T','Port2_face','Port2_T'}; bnd.curofforbeta = 'beta1'; bnd.sigmabnd = 0; bnd.wavetype = 'plane'; bnd.sparammethod = {'energy','field','field','field','energy','field'}; bnd.portnr = {1,1,1,1,2,2}; bnd.nbnd = 1; bnd.Pphase = 0; bnd.symtypez = '-1'; bnd.symtypey = '-1'; bnd.H0 = {{0;0;0}}; bnd.symtypex = '-1'; bnd.ah = {{0;0;1}}; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,1,3,3,1,3, ... 3,2,3,3,4,3,3,3,3,3,4,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,5,5,5,5,5,5,5,5,5,5,6,6,5,5,5,5,5,5]; appl.bnd = bnd; clear equ equ.Sd = {{'Sdx_guess_rfw';'Sdy_guess_rfw';'Sdz_guess_rfw'}}; equ.magconstrel = 'mur'; equ.srcpnt = {{0;0;0}}; equ.M = {{0;0;0}}; equ.S0 = {{0;0;0}}; equ.gporder = 1; equ.coordOn = {{0;0;0}}; equ.P = {{0;0;0}}; equ.sigma = {'mat3_sigma',0,'mat6_sigma'}; equ.dinit = 0; equ.epsilonr = {'mat3_epsilonr',3,1}; equ.name = {'M','R','Air'}; equ.dr = 'dr_guess_rfw'; equ.rOn = 0; equ.cporder = 1; equ.mur = {'mat3_mur',1,1}; equ.normfH = '1/mu0_rfw*normB_rfw'; equ.Br = {{0;0;0}}; equ.n = 1; equ.init = {{0;0;0;0;0;0;0;0;0;0;0;0;0;0;0; ... 'psi0_rfw'}}; equ.Stype = 'none'; equ.shape = [1;2]; equ.R0 = 'R0_guess_rfw'; equ.elconstrel = 'epsr'; equ.fH = {{'1/mu0_rfw*Bx_rfw';'1/mu0_rfw*By_rfw';'1/mu0_rfw*Bz_rfw'}}; equ.matparams = 'epsr'; equ.Dr = {{0;0;0}}; equ.usage = 1; equ.srcaxis = {{0;0;1}}; equ.user = {{0;0;0}}; equ.ind = [1,1,1,1,1,1,2,1,3,1,1,1,1,1,1,1,1,1]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'E0ix','exp(-j*k0_rfw*z)', ... 'E0iy','0', ... 'E0iz','0', ... 'psi0','psi0_guess_rfw'}; fem.appl{1} = appl; % Application mode 2 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en','hn','ex','ey','ez','hx','hy','hz'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex'',''ey'',''ez''})','shlag(2,''en'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {'mat4_mur','mat4_mur',1,1,1}; bnd.matparams = {'n','n','n','epsr','n'}; bnd.sigma = {'mat4_sigma','mat4_sigma',0,0,0}; bnd.epsilonr = {'mat4_epsilonr','mat4_epsilonr',1,3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {1,0,0,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,4,3,3,1,3,3,5,3,3,1,3, ... 3,2,3,3,1,3,3,3,3,3,1,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,3,3,3,3,3,3,3,3,5,3,3,3,3,3,3,3,3,3]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{2} = appl; % Application mode 3 clear appl appl.mode.class = 'BoundaryModeAnalysis'; appl.mode.type = 'cartesian'; appl.dim = {'en2','hn2','ex2','ey2','ez2','hx2','hy2','hz2'}; appl.sdim = {'x','y','z'}; appl.name = 'rfwb2'; appl.module = 'RF'; appl.shape = {'shcurl(2,{''ex2'',''ey2'',''ez2''})','shlag(2,''en2'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_rfwb2'; clear prop prop.elemdefault='Vec2_lag2'; prop.field='TETM'; prop.inputvar='nu'; prop.solvefor='E'; prop.eigtype='manual'; prop.frame='ref'; prop.constrtype='ideal'; appl.prop = prop; clear edg edg.name = ''; edg.type = {'cont','E0'}; edg.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1,2,1,2, ... 1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1, ... 1,2,2,2,2,2,2]; appl.edg = edg; clear bnd bnd.cporder = 1; bnd.gporder = 1; bnd.mur = {1,'mat3_mur',1,1,'mat3_mur',1,1}; bnd.matparams = {'epsr','n','n','n','epsr','epsr','n'}; bnd.sigma = {0,'mat3_sigma',0,'5.998e7[S/m]','mat3_sigma',0,0}; bnd.epsilonr = {3,'mat3_epsilonr',1,1,'mat3_epsilonr',3,1}; bnd.name = ''; bnd.n = 1; bnd.usage = {0,0,0,0,1,1,1}; bnd.init = 0; bnd.shape = [1;2]; bnd.ind = [1,2,2,1,2,3,1,2,3,1,2,3,1,2,3,2,1,3,2,1,3,3,1,3,3,7,3,3,1,3, ... 3,2,3,3,4,3,3,3,3,3,4,3,3,3,3,3,1,3,3,3,1,3,2,1,3,3,1,3,3,1,3,3,1,3,3, ... 2,2,2,2,2,2,5,5,5,5,5,5,6,5,7,5,5,5,5,5,5,5,5,5]; appl.bnd = bnd; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7', ... 'nu','1e9', ... 'beta','30'}; fem.appl{3} = appl; fem.sdim = {'x','y','z'}; fem.frame = {'ref'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Scalar expressions fem.expr = {}; % Global expressions fem.globalexpr = {}; % Functions clear fcns fem.functions = {}; % Solution form fem.solform = 'weak'; % Library materials clear lib lib.mat{1}.name='Copper'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='nu(T[1/K])'; lib.mat{1}.variables.res='res_solid_1(T[1/K])[ohm*m]'; lib.mat{1}.variables.E='E(T[1/K])[Pa]'; lib.mat{1}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{1}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{1}.variables.VP='VP_solid_1(T[1/K])[Pa]'; lib.mat{1}.variables.HC='HC_solid_1(T[1/K])[J/(mol*K)]'; lib.mat{1}.variables.C='C_solid_1(T[1/K])[J/(kg*K)]'; lib.mat{1}.variables.kappa='kappa(T[1/K])[Pa]'; lib.mat{1}.variables.mu='mu(T[1/K])[Pa]'; lib.mat{1}.variables.k='k_solid_181_nm_thin_film_8(T[1/K])[W/(m*K)]'; lib.mat{1}.variables.CTE='CTE_solid_1(T[1/K])[1/K]'; lib.mat{1}.variables.sigma='sigma_solid_1(T[1/K])[S/m]'; lib.mat{1}.variables.dL='dL_solid_1(T[1/K])-dL_solid_1(Tempref[1/K])'; lib.mat{1}.variables.alpha='alpha_solid_1(T[1/K])[1/K]+(Tempref-293[K])/(T-Tempref)*(alpha_solid_1(T[1/K])[1/K]-alpha_solid_1(Tempref[1/K])[1/K])'; lib.mat{1}.variables.epsilon='epsilon_solid_polished_2(T[1/K])'; lib.mat{1}.variables.Syt='Syt_solid_40_reduction_by_cold_drawing_5(T[1/K])[Pa]'; lib.mat{1}.variables.elong='elong_solid_40_reduction_by_cold_drawing_2(T[1/K])'; lib.mat{1}.variables.rho='rho_solid_1(T[1/K])[kg/m^3]'; lib.mat{1}.variables.nemiss='nemiss(T[1/K])'; lib.mat{1}.variables.Sys='Sys_solid_40_reduction_by_cold_drawing_4(T[1/K])[Pa]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='dL_solid_1(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-0.003272586','1','-6.837087E-8','2','1.574823E-8','3', ... '3.040518E-10'},{'0','-0.003491523','1','2.12144E-6','2','5.197613E-8','3', ... '-6.339761E-11'},{'0','-0.004540862','1','1.446717E-5','2','3.415834E-9','3', ... '3.472655E-13'}}; fcns{1}.intervals={'4.0','80.0','282.0','1250.0'}; fcns{2}.type='piecewise'; fcns{2}.name='dL_liquid_2(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','-0.03841182','1','2.563914E-5','2','1.948782E-9'}}; fcns{2}.intervals={'1358.0','1523.0'}; fcns{3}.type='piecewise'; fcns{3}.name='CTE_solid_1(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','-8.574809E-9','1','4.13567E-9','2','-5.673583E-10','3', ... '5.520915E-11'},{'0','2.194122E-7','1','-2.662325E-8','2','4.800942E-10','3', ... '6.093443E-11','4','-6.195564E-13'},{'0','-8.81E-6','1','3.292355E-7','2', ... '-1.773823E-9','3','4.545667E-12','4','-4.483983E-15'},{'0','9.897871E-6','1', ... '3.796303E-8','2','-6.61053E-11','3','5.60845E-14','4','-1.591449E-17'}}; fcns{3}.intervals={'4.0','13.0','60.0','300.0','1250.0'}; fcns{4}.type='piecewise'; fcns{4}.name='CTE_liquid_2(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','2.563914E-5','1','3.897564E-9'}}; fcns{4}.intervals={'1358.0','1523.0'}; fcns{5}.type='piecewise'; fcns{5}.name='k_solid_residual_resistivity_ratio_of_30_1(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','12.55868','1','36.66487','2','1.387207','3', ... '-0.07168113','4','6.99799E-4'},{'0','2174.919','1','-45.25448','2', ... '0.3738471','3','-9.504397E-4'},{'0','2545.87','1','-67.53869','2', ... '0.8176488','3','-0.004470238','4','9.22619E-6'},{'0','555.4','1','-2.116905', ... '2','0.008971429','3','-1.266667E-5'},{'0','423.7411','1','-0.3133575','2', ... '0.001013916','3','-1.570451E-6','4','1.06222E-9','5','-2.64198E-13'}}; fcns{5}.intervals={'1.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{6}.type='piecewise'; fcns{6}.name='k_solid_residual_resistivity_ratio_of_100_2(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-22.5','1','135.0796','2','4.741986','3','-0.3723024', ... '4','0.004720439'},{'0','3933.429','1','-63.68','2','0.05142857'},{'0','6328.994', ... '1','-201.2242','2','2.37446','3','-0.009554548'},{'0','4760.0','1', ... '-147.1793','2','1.922369','3','-0.01129286','4','2.488095E-5'},{'0','831.0', ... '1','-6.986667','2','0.04406667','3','-1.253333E-4','4','1.333333E-7'},{'0', ... '528.9926','1','-1.034752','2','0.003059339','3','-4.399776E-6','4', ... '2.929135E-9','5','-7.326451E-13'}}; fcns{6}.intervals={'1.0','30.0','40.0','70.0','100.0','300.0','1358.0'}; fcns{7}.type='piecewise'; fcns{7}.name='k_solid_residual_resistivity_ratio_of_300_3(T)'; fcns{7}.extmethod='const'; fcns{7}.subtype='poly'; fcns{7}.expr={{'0','43.92216','1','471.9349','2','8.879346','3','-1.556526', ... '4','0.02860221'},{'0','11974.61','1','-403.36','2','3.765714'},{'0','9962.794', ... '1','-348.0243','2','4.358806','3','-0.01844096'},{'0','5053.0','1', ... '-154.0752','2','1.977238','3','-0.01141905','4','2.47619E-5'},{'0','950.0', ... '1','-9.188333','2','0.06011667','3','-1.766667E-4','4','1.933333E-7'},{'0', ... '654.0162','1','-2.114367','2','0.006545992','3','-9.503517E-6','4', ... '6.375282E-9','5','-1.604293E-12'}}; fcns{7}.intervals={'1.0','25.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{8}.type='piecewise'; fcns{8}.name='k_solid_residual_resistivity_ratio_of_1000_4(T)'; fcns{8}.extmethod='const'; fcns{8}.subtype='poly'; fcns{8}.expr={{'0','43.5812','1','1287.778','2','127.4809','3','-18.90287', ... '4','0.5278154'},{'0','23251.23','1','-934.5617','2','10.06102'},{'0','12192.48', ... '1','-440.2468','2','5.626285','3','-0.02418948'},{'0','5527.0','1', ... '-171.526','2','2.221036','3','-0.01292619','4','2.821429E-5'},{'0','907.0', ... '1','-7.941667','2','0.04885','3','-1.353333E-4','4','1.4E-7'},{'0', ... '437.5628','1','-0.1648376','2','1.824664E-4','3','-1.427409E-7','4', ... '3.979442E-11'}}; fcns{8}.intervals={'1.0','18.0','45.0','70.0','100.0','300.0','1358.0'}; fcns{9}.type='piecewise'; fcns{9}.name='k_solid_residual_resistivity_ratio_of_3000_5(T)'; fcns{9}.extmethod='const'; fcns{9}.subtype='poly'; fcns{9}.expr={{'0','936.8333','1','3199.781','2','718.3418','3','-124.0868', ... '4','4.473485'},{'0','43533.03','1','-1969.955','2','12.47834','3', ... '0.3350561'},{'0','40360.93','1','-2208.569','2','42.18538','3','-0.2725321'},{'0', ... '16075.33','1','-709.3282','2','12.42221','3','-0.09815779','4', ... '2.927777E-4'},{'0','1135.071','1','-13.04691','2','0.08980613','3', ... '-2.750007E-4','4','3.115546E-7'},{'0','673.4937','1','-2.249547','2', ... '0.006928375','3','-1.001266E-5','4','6.69616E-9','5','-1.68138E-12'}}; fcns{9}.intervals={'1.0','10.0','30.0','45.0','100.0','300.0','1358.0'}; fcns{10}.type='piecewise'; fcns{10}.name='k_solid_120_nm_thin_film_6(T)'; fcns{10}.extmethod='const'; fcns{10}.subtype='poly'; fcns{10}.expr={{'0','291.9251','1','-0.5765848','2','0.001195407'},{'0', ... '224.1887','1','0.03455938','2','-1.829181E-4'}}; fcns{10}.intervals={'100.0','225.0','475.0'}; fcns{11}.type='piecewise'; fcns{11}.name='k_solid_300_nm_thin_film_7(T)'; fcns{11}.extmethod='const'; fcns{11}.subtype='poly'; fcns{11}.expr={{'0','504.4357','1','-1.860341','2','0.006224168','3', ... '-7.062428E-6'},{'0','296.6006','1','0.1293918','2','-2.169443E-4'}}; fcns{11}.intervals={'100.0','300.0','475.0'}; fcns{12}.type='piecewise'; fcns{12}.name='k_solid_181_nm_thin_film_8(T)'; fcns{12}.extmethod='const'; fcns{12}.subtype='poly'; fcns{12}.expr={{'0','332.2834','1','-0.5270418','2','0.001062584'},{'0', ... '273.4186','1','-0.004096151','2','-8.062265E-5'}}; fcns{12}.intervals={'100.0','200.0','475.0'}; fcns{13}.type='piecewise'; fcns{13}.name='k_liquid_9(T)'; fcns{13}.extmethod='const'; fcns{13}.subtype='poly'; fcns{13}.expr={{'0','45.32857','1','0.1504997','2','-5.704651E-5','3', ... '9.576806E-9','4','-8.501398E-13','5','3.056993E-17'}}; fcns{13}.intervals={'1358.0','8500.0'}; fcns{14}.type='piecewise'; fcns{14}.name='E(T)'; fcns{14}.extmethod='const'; fcns{14}.subtype='poly'; fcns{14}.expr={{'0','1.37E11','1','-3.330669E-6','2','-127000.0'},{'0', ... '1.408492E11','1','-4.703751E7','2','-12923.82'}}; fcns{14}.intervals={'4.0','300.0','1250.0'}; fcns{15}.type='piecewise'; fcns{15}.name='res_solid_1(T)'; fcns{15}.extmethod='const'; fcns{15}.subtype='poly'; fcns{15}.expr={{'0','2.0E-11'},{'0','1.002557E-11','1','2.945503E-12','2', ... '-2.767806E-13','3','8.665115E-15'},{'0','1.370786E-9','1','-8.741734E-11', ... '2','1.738251E-12','3','-6.532611E-15'},{'0','-3.514582E-9','1', ... '7.064722E-11','2','-8.917638E-15','3','1.026538E-17'}}; fcns{15}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{16}.type='piecewise'; fcns{16}.name='res_liquid_2(T)'; fcns{16}.extmethod='const'; fcns{16}.subtype='poly'; fcns{16}.expr={{'0','7.508256E-8','1','9.942937E-11'}}; fcns{16}.intervals={'1358.0','1799.0'}; fcns{17}.type='piecewise'; fcns{17}.name='epsilon_solid_oxidized_1(T)'; fcns{17}.extmethod='const'; fcns{17}.subtype='poly'; fcns{17}.expr={{'0','1.036246','1','-0.001938284','2','1.708638E-6'}}; fcns{17}.intervals={'588.0','1033.0'}; fcns{18}.type='piecewise'; fcns{18}.name='epsilon_solid_polished_2(T)'; fcns{18}.extmethod='const'; fcns{18}.subtype='poly'; fcns{18}.expr={{'0','0.0027','1','2.72E-5'}}; fcns{18}.intervals={'293.0','750.0'}; fcns{19}.type='piecewise'; fcns{19}.name='Syt_solid_annealed_65_micron_GS__1(T)'; fcns{19}.extmethod='const'; fcns{19}.subtype='poly'; fcns{19}.expr={{'0','4.397735E8','1','-1138269.0','2','1362.768'}}; fcns{19}.intervals={'4.0','295.0'}; fcns{20}.type='piecewise'; fcns{20}.name='Syt_solid_10_cold_rolled_2(T)'; fcns{20}.extmethod='const'; fcns{20}.subtype='poly'; fcns{20}.expr={{'0','2.341782E8','1','377241.4','2','-1269.352','3', ... '0.6508134'}}; fcns{20}.intervals={'293.0','873.0'}; fcns{21}.type='piecewise'; fcns{21}.name='Syt_solid_annealed_120_micron_GS__3(T)'; fcns{21}.extmethod='const'; fcns{21}.subtype='poly'; fcns{21}.expr={{'0','3.574227E8','1','-732818.0','2','1558.538','3', ... '-2.478229','4','0.001329502'}}; fcns{21}.intervals={'293.0','922.0'}; fcns{22}.type='piecewise'; fcns{22}.name='Syt_solid_annealed_12_micron_GS__4(T)'; fcns{22}.extmethod='const'; fcns{22}.subtype='poly'; fcns{22}.expr={{'0','4.317654E8','1','-642027.4','2','-68.89019'}}; fcns{22}.intervals={'30.0','300.0'}; fcns{23}.type='piecewise'; fcns{23}.name='Syt_solid_40_reduction_by_cold_drawing_5(T)'; fcns{23}.extmethod='const'; fcns{23}.subtype='poly'; fcns{23}.expr={{'0','-1.477479E9','1','1.932506E7','2','-74594.2','3', ... '125.2704','4','-0.078893'},{'0','5.596969E8','1','-994802.5','2','453.4515'}}; fcns{23}.intervals={'293.0','588.0','1088.0'}; fcns{24}.type='piecewise'; fcns{24}.name='elong_solid_annealed_120_micron_GS__1(T)'; fcns{24}.extmethod='const'; fcns{24}.subtype='poly'; fcns{24}.expr={{'0','123.3713','1','-0.2188266','2','1.120172E-4'}}; fcns{24}.intervals={'293.0','922.0'}; fcns{25}.type='piecewise'; fcns{25}.name='elong_solid_40_reduction_by_cold_drawing_2(T)'; fcns{25}.extmethod='const'; fcns{25}.subtype='poly'; fcns{25}.expr={{'0','53.2536','1','-0.3009904','2','6.663194E-4','3', ... '-3.897456E-7'}}; fcns{25}.intervals={'293.0','1088.0'}; fcns{26}.type='piecewise'; fcns{26}.name='alpha_solid_1(T)'; fcns{26}.extmethod='const'; fcns{26}.subtype='poly'; fcns{26}.expr={{'0','1.104402E-5','1','4.812192E-8','2','-1.223083E-10'},{'0', ... '1.276495E-5','1','1.849516E-8','2','1.203963E-11','3','-1.023671E-13'},{'0', ... '1.54043E-5','1','4.517462E-9','2','-5.067436E-13'}}; fcns{26}.intervals={'4.0','100.0','230.0','1250.0'}; fcns{27}.type='piecewise'; fcns{27}.name='alpha_liquid_2(T)'; fcns{27}.extmethod='const'; fcns{27}.subtype='poly'; fcns{27}.expr={{'0','2.829819E-5','1','1.940378E-9'}}; fcns{27}.intervals={'1358.0','1523.0'}; fcns{28}.type='piecewise'; fcns{28}.name='C_solid_1(T)'; fcns{28}.extmethod='const'; fcns{28}.subtype='poly'; fcns{28}.expr={{'0','0.008168055','1','0.00104457','2','0.003441219','3', ... '2.847033E-4','4','2.246429E-5'},{'0','29.05972','1','-3.767169','2', ... '0.1540539','3','-0.001048364','4','3.010206E-7'},{'0','-215.2814','1', ... '8.236392','2','-0.04732108','3','1.291112E-4','4','-1.357031E-7'},{'0', ... '342.764','1','0.1338348','2','5.535252E-5','3','-1.971221E-7','4', ... '1.140747E-10'}}; fcns{28}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{29}.type='piecewise'; fcns{29}.name='C_liquid_2(T)'; fcns{29}.extmethod='const'; fcns{29}.subtype='poly'; fcns{29}.expr={{'0','516.1615'}}; fcns{29}.intervals={'1356.0','6000.0'}; fcns{30}.type='piecewise'; fcns{30}.name='C_gas_3(T)'; fcns{30}.extmethod='const'; fcns{30}.subtype='poly'; fcns{30}.expr={{'0','327.0843','1','3.888545E-5'},{'0','309.7379','1', ... '0.04659834','2','-4.21684E-5','3','1.304115E-8','4','-1.086767E-13'}}; fcns{30}.intervals={'293.0','1000.0','2000.0'}; fcns{31}.type='piecewise'; fcns{31}.name='HC_solid_1(T)'; fcns{31}.extmethod='const'; fcns{31}.subtype='poly'; fcns{31}.expr={{'0','5.190474E-4','1','6.637828E-5','2','2.186757E-4','3', ... '1.809176E-5','4','1.427516E-6'},{'0','1.846629','1','-0.2393885','2', ... '0.00978951','3','-6.661932E-5','4','1.912866E-8'},{'0','-13.68027','1', ... '0.5233899','2','-0.003007065','3','8.204498E-6','4','-8.623391E-9'},{'0', ... '21.78128','1','0.008504666','2','3.517431E-6','3','-1.252632E-8','4', ... '7.248993E-12'}}; fcns{31}.intervals={'1.0','18.0','60.0','300.0','1300.0'}; fcns{32}.type='piecewise'; fcns{32}.name='HC_liquid_2(T)'; fcns{32}.extmethod='const'; fcns{32}.subtype='poly'; fcns{32}.expr={{'0','32.8'}}; fcns{32}.intervals={'1356.0','6000.0'}; fcns{33}.type='piecewise'; fcns{33}.name='HC_gas_3(T)'; fcns{33}.extmethod='const'; fcns{33}.subtype='poly'; fcns{33}.expr={{'0','20.7849','1','2.471015E-6'},{'0','19.6826','1','0.002961136', ... '2','-2.679634E-6','3','8.287132E-10','4','-6.905968E-15'}}; fcns{33}.intervals={'293.0','1000.0','2000.0'}; fcns{34}.type='piecewise'; fcns{34}.name='mu(T)'; fcns{34}.extmethod='const'; fcns{34}.subtype='poly'; fcns{34}.expr={{'0','5.12E10','1','4.718448E-7','2','-46300.0'}}; fcns{34}.intervals={'4.0','300.0'}; fcns{35}.type='piecewise'; fcns{35}.name='sigma_solid_1(T)'; fcns{35}.extmethod='const'; fcns{35}.subtype='general'; fcns{35}.expr={'1/(2.000000E-11)', ... '1/(8.665115E-15*T^3-2.767806E-13*T^2+2.945503E-12*T+1.002557E-11)', ... '1/(-6.532611E-15*T^3+1.738251E-12*T^2-8.741734E-11*T+1.370786E-09)', ... '1/(1.026538E-17*T^3-8.917638E-15*T^2+7.064722E-11*T-3.514582E-09)'}; fcns{35}.intervals={'1.0','7.0','40.0','100.0','1358.0'}; fcns{36}.type='piecewise'; fcns{36}.name='sigma_liquid_2(T)'; fcns{36}.extmethod='const'; fcns{36}.subtype='general'; fcns{36}.expr={'1/(9.942937E-11*T+7.508256E-08)'}; fcns{36}.intervals={'1358.0','1799.0'}; fcns{37}.type='piecewise'; fcns{37}.name='nemiss(T)'; fcns{37}.extmethod='const'; fcns{37}.subtype='poly'; fcns{37}.expr={{'0','1.037439','1','-0.001949328','2','1.683428E-6'}}; fcns{37}.intervals={'588.0','1033.0'}; fcns{38}.type='piecewise'; fcns{38}.name='Sys_solid_annealed_42_micron_GS__1(T)'; fcns{38}.extmethod='const'; fcns{38}.subtype='poly'; fcns{38}.expr={{'0','3.470962E7','1','-16299.27'}}; fcns{38}.intervals={'4.0','300.0'}; fcns{39}.type='piecewise'; fcns{39}.name='Sys_solid_10_cold_rolled_2(T)'; fcns{39}.extmethod='const'; fcns{39}.subtype='poly'; fcns{39}.expr={{'0','3.294455E8','1','-1297557.0','2','5249.353','3', ... '-8.82769','4','0.004626405'}}; fcns{39}.intervals={'293.0','873.0'}; fcns{40}.type='piecewise'; fcns{40}.name='Sys_solid_annealed_120_micron_GS__3(T)'; fcns{40}.extmethod='const'; fcns{40}.subtype='poly'; fcns{40}.expr={{'0','9.917962E7','1','-276037.4','2','304.3743','3', ... '-0.1255723'}}; fcns{40}.intervals={'293.0','922.0'}; fcns{41}.type='piecewise'; fcns{41}.name='Sys_solid_40_reduction_by_cold_drawing_4(T)'; fcns{41}.extmethod='const'; fcns{41}.subtype='poly'; fcns{41}.expr={{'0','3.648E8','1','3198918.0','2','-24450.6','3','60.15024', ... '4','-0.04997051'},{'0','1.156124E10','1','-5.101785E7','2','75136.57','3', ... '-36.86067'},{'0','3.571834E8','1','-1037630.0','2','1021.334','3', ... '-0.3372394'}}; fcns{41}.intervals={'293.0','588.0','644.0','1088.0'}; fcns{42}.type='piecewise'; fcns{42}.name='rho_solid_1(T)'; fcns{42}.extmethod='const'; fcns{42}.subtype='poly'; fcns{42}.expr={{'0','9028.155','1','0.001936185','2','-4.310034E-4','3', ... '-8.227902E-6'},{'0','9034.264','1','-0.05885933','2','-0.001406238','3', ... '1.736657E-6'},{'0','9062.604','1','-0.3926111','2','-8.730517E-5'}}; fcns{42}.intervals={'4.0','90.0','250.0','1250.0'}; fcns{43}.type='piecewise'; fcns{43}.name='rho_liquid_2(T)'; fcns{43}.extmethod='const'; fcns{43}.subtype='poly'; fcns{43}.expr={{'0','8938.719','1','-0.7367'}}; fcns{43}.intervals={'1358.0','1523.0'}; fcns{44}.type='piecewise'; fcns{44}.name='TD(T)'; fcns{44}.extmethod='const'; fcns{44}.subtype='poly'; fcns{44}.expr={{'0','1.952783E-5','1','1.293564E-8'}}; fcns{44}.intervals={'1358.0','1473.0'}; fcns{45}.type='piecewise'; fcns{45}.name='VP_solid_1(T)'; fcns{45}.extmethod='const'; fcns{45}.subtype='general'; fcns{45}.expr={'(exp((-1.774800e+004/T-7.317000e-001*log10(T)+1.200381e+001)*log(10.0)))*1.333200e+002'}; fcns{45}.intervals={'293.0','1358.0'}; fcns{46}.type='piecewise'; fcns{46}.name='VP_liquid_2(T)'; fcns{46}.extmethod='const'; fcns{46}.subtype='general'; fcns{46}.expr={'(exp((-1.641500e+004/T+8.729810e+000)*log(10.0)))*1.333200e+002'}; fcns{46}.intervals={'1358.0','1850.0'}; fcns{47}.type='piecewise'; fcns{47}.name='nu(T)'; fcns{47}.extmethod='const'; fcns{47}.subtype='poly'; fcns{47}.expr={{'0','0.3378748','1','7.672235E-7','2','-3.529109E-8'}}; fcns{47}.intervals={'4.0','300.0'}; fcns{48}.type='piecewise'; fcns{48}.name='kappa(T)'; fcns{48}.extmethod='const'; fcns{48}.subtype='poly'; fcns{48}.expr={{'0','1.408545E11','1','-151138.5','2','-155999.5'}}; fcns{48}.intervals={'4.0','300.0'}; fcns{49}.type='piecewise'; fcns{49}.name='eta(T)'; fcns{49}.extmethod='const'; fcns{49}.subtype='poly'; fcns{49}.expr={{'0','0.02795433','1','-2.813626E-5','2','7.916142E-9'}}; fcns{49}.intervals={'1373.0','1473.0'}; lib.mat{1}.functions = fcns; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.TD='TD(T[1/K])[m^2/s]'; lib.mat{2}.variables.C='C(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; clear fcns fcns{1}.type='piecewise'; fcns{1}.name='k(T)'; fcns{1}.extmethod='const'; fcns{1}.subtype='poly'; fcns{1}.expr={{'0','-8.404165E-4','1','1.107418E-4','2','-8.635537E-8','3', ... '6.31411E-11','4','-1.88168E-14'}}; fcns{1}.intervals={'70.0','1000.0'}; fcns{2}.type='piecewise'; fcns{2}.name='C(T)'; fcns{2}.extmethod='const'; fcns{2}.subtype='poly'; fcns{2}.expr={{'0','1010.97','1','0.0439479','2','-2.922398E-4','3', ... '6.503467E-7'},{'0','1093.29','1','-0.6355521','2','0.001633992','3', ... '-1.412935E-6','4','5.59492E-10','5','-8.663072E-14'},{'0','701.0807','1', ... '0.8493867','2','-5.846487E-4','3','2.302436E-7','4','-4.846758E-11','5', ... '4.23502E-15'}}; fcns{2}.intervals={'100.0','375.0','1300.0','3000.0'}; fcns{3}.type='piecewise'; fcns{3}.name='rho(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'-1','352.716'}}; fcns{3}.intervals={'80.0','3000.0'}; fcns{4}.type='piecewise'; fcns{4}.name='TD(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','1.713214E-4','1','-1.204913E-6','2','2.839046E-9','3', ... '-1.532799E-12'},{'0','0.00416418','1','-1.191227E-5','2','8.863636E-9'}}; fcns{4}.intervals={'300.0','753.0','873.0'}; fcns{5}.type='piecewise'; fcns{5}.name='eta(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-1.132275E-7','1','7.94333E-8','2','-7.197989E-11','3', ... '5.158693E-14','4','-1.592472E-17'},{'0','3.892629E-6','1','5.75387E-8','2', ... '-2.675811E-11','3','9.709691E-15','4','-1.355541E-18'}}; fcns{5}.intervals={'120.0','600.0','2150.0'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Copper_1'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.nu='0.35'; lib.mat{3}.variables.alphares='0.0039[1/K]'; lib.mat{3}.variables.E='110e9[Pa]'; lib.mat{3}.variables.mur='1'; lib.mat{3}.variables.sigma='5.998e7[S/m]'; lib.mat{3}.variables.epsilonr='1'; lib.mat{3}.variables.alpha='17e-6[1/K]'; lib.mat{3}.variables.C='385[J/(kg*K)]'; lib.mat{3}.variables.res0='1.72e-8[ohm*m]'; lib.mat{3}.variables.rho='8700[kg/m^3]'; lib.mat{3}.variables.k='400[W/(m*K)]'; lib.mat{3}.variables.T0='298[K]'; lib.mat{4}.name='Copper_2'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.nu='0.35'; lib.mat{4}.variables.alphares='0.0039[1/K]'; lib.mat{4}.variables.E='110e9[Pa]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.alpha='17e-6[1/K]'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='298[K]'; lib.mat{5}.name='Air_1'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{5}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{5}.variables.gamma='1.4'; lib.mat{5}.variables.sigma='0[S/m]'; lib.mat{5}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{5}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{5}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{5}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{5}.functions = fcns; lib.mat{6}.name='Air_2'; lib.mat{6}.varname='mat6'; lib.mat{6}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{6}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{6}.variables.gamma='1.4'; lib.mat{6}.variables.sigma='0[S/m]'; lib.mat{6}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{6}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{6}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{6}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{6}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Generate GMG mesh cases fem=meshcaseadd(fem,'mcaseorig',0,'mgauto','shape','meshscale',2.0,'mggeom',[1],'nmcases',1,'shapechg',-1,'rmethod','regular','defaults','on'); % Extend mesh fem.xmesh=meshextend(fem, ... 'geoms',[1], ... 'eqvars','on', ... 'cplbndeq','on', ... 'cplbndsh','off', ... 'linshape',[1], ... 'linshapetol',0.1); % Evaluate initial value using current solution init = asseminit(fem,'u',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','complexfun','on','matherr','on'); % Mapping current solution to current extended mesh u = asseminit(fem,'init',fem0.sol,'xmesh',fem0.xmesh,'blocksize','auto','matherr','on'); % Solve problem fem.sol=femstatic(fem, ... 'init',init, ... 'u',u, ... 'method','eliminate', ... 'nullfun','auto', ... 'complexfun','on', ... 'matherr','on', ... 'solfile','on', ... 'conjugate','off', ... 'symmetric','auto', ... 'solcomp',{'tExEyEz10','tExEyEz20','tExEyEz21'}, ... 'outcomp',{'texeyez10','texeyez21','texeyez20','tex2ey2ez220','tex2ey2ez221','en','en2','tExEyEz10','tExEyEz20','tExEyEz21','tex2ey2ez210'}, ... 'rowscale','on', ... 'blocksize','auto', ... 'reacf','on', ... 'ntol',1.0E-6, ... 'maxiter',25, ... 'nonlin','auto', ... 'damping','on', ... 'hnlin','off', ... 'linsolver','gmres', ... 'itol',1.0E-6, ... 'rhob',400.0, ... 'maxlinit',10000, ... 'itrestart',50, ... 'prefuntype','right', ... 'prefun','gmg', ... 'prepar',{'iter',2,'mgcycle','v','mgassem',[1 1],'presmooth','sorvec','presmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'postsmooth','soruvec','postsmoothpar',{'iter',2,'relax',1.0,'sorblocked','on','seconditer',2},'csolver','pardiso','csolverpar',{'pardreorder','nd','pardrreorder','on','pivotstrategy','off','pivotperturb','1.0E-8','itol',0.1,'rhob',1,'errorchk','on'}}, ... 'uscale','auto', ... 'mcase',[0 1]); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'slicedata',{'Ey','cont','internal','recover','off','unit','V/m'}, ... 'slicexspacing',1, ... 'sliceyspacing',0, ... 'slicezspacing',0, ... 'sliceedgestyle','none', ... 'slicefacestyle','interp', ... 'slicebar','on', ... 'slicemap','jet(1024)', ... 'slicemapstyle','auto', ... 'solnum','end', ... 'phase',0, ... 'title','Slice: Electric field, y component [V/m]', ... 'refine','auto', ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]}, ... 'complexfun','on', ... 'matherr','off', ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','on', ... 'camlight','off', ... 'scenelight','off', ... 'campos',[-0.011953390520730477,-0.013635768136577449,0.011963214219750978], ... 'camtarget',[2.500000118743628E-4,0.002268000040203333,3.8949999725446105E-4], ... 'camup',[0,0,1], ... 'camva',7.303033957978463, ... 'camprojection','orthographic', ... 'transparency',1.0); % Remove generated GMG mesh cases fem=meshcasedel(fem,[1],'defaults','on');