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why we do meshing in comsol?
Posted Mar 16, 2010, 3:58 p.m. EDT 2 Replies
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hi all,
I have one question that why we do meshing in comsol and why we some times refine meshing on specific
boundaries?
i hope you people give me detail idea and logic of meshing.
Thanks
I have one question that why we do meshing in comsol and why we some times refine meshing on specific
boundaries?
i hope you people give me detail idea and logic of meshing.
Thanks
2 Replies Last Post Mar 18, 2010, 3:12 a.m. EDT
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Posted:
1 decade ago
Hi
I would answer because COMSOL is based on FEM where we represent any geoemtry by (close to infinitely) small elements.
To get a better understanding, read through "The Finite Element Method" by D.W. Pepper J.C. Heinrich, Taylor&Francis, 2006, and "Introduction to comuptation and Modeling for Differential Equations", by L. Edsberg, Wiley, 2008. These book refer also to COMSOL and have a notation close to the one of COMSOL.
Have a nice reading
Ivar
I would answer because COMSOL is based on FEM where we represent any geoemtry by (close to infinitely) small elements.
To get a better understanding, read through "The Finite Element Method" by D.W. Pepper J.C. Heinrich, Taylor&Francis, 2006, and "Introduction to comuptation and Modeling for Differential Equations", by L. Edsberg, Wiley, 2008. These book refer also to COMSOL and have a notation close to the one of COMSOL.
Have a nice reading
Ivar
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Posted:
1 decade ago
Please refer
www.colorado.edu/engineering/cas/courses.d/IFEM.d/
(It is nicely written)
The basic concept is the subdivision of the mathematical model into non-overlapping components called elements. The response of each element is expressed by unknown functions and the response of the whole model is then considered to be approximated by assembling the collection of all elements. Therefore, Finite-element requires discretization of the domain. We do that by meshing it, so that, we would have nodal representation of the geometry and functional representation of the domain. And, FEM is heavily mesh dependent. Refining is needed for two main reasons. One geometrical and other is mathematical.
Geometric > i.e., if you have curved edges, you will have better representation with smaller elements. Example, you have a circle, and you want to represent it by using straight lines. Obviously, result will be closer to actual circle, if you use higher number of smaller sized lines.
REFER > www.colorado.edu/engineering/cas/courses.d/IFEM.d/IFEM.Ch01.d/IFEM.Ch01.pdf
and slide to Page 1-6. There are some visuals.
Mathematical > In finite difference, we get the solution on the grid points only. In Finite Element, we get the solution over the domain (i.e. at the nodes and anywhere in between). Now, unlike FDM, to get the solution on entire element, we use piecewise and well-behaved shape functions to interpolate from integration points. So, lets say you have a quadratic shape function and very large elements; while going from one node to another node, you might not be able to capture the whole transition. However, if you have smaller elements with same degreed shape functions, you will have a better representation. Lets say, axially loaded plate with a center hole on it. We know that there will be a stress gradient around the hole. We need to use an adaptivity or denser meshes in that area to get the better presentation. Or you can still use coarser mesh but then you should to use higher order polynomials for interpolation. These two called, h-method and p-method.
I hope it helps.
www.colorado.edu/engineering/cas/courses.d/IFEM.d/
(It is nicely written)
The basic concept is the subdivision of the mathematical model into non-overlapping components called elements. The response of each element is expressed by unknown functions and the response of the whole model is then considered to be approximated by assembling the collection of all elements. Therefore, Finite-element requires discretization of the domain. We do that by meshing it, so that, we would have nodal representation of the geometry and functional representation of the domain. And, FEM is heavily mesh dependent. Refining is needed for two main reasons. One geometrical and other is mathematical.
Geometric > i.e., if you have curved edges, you will have better representation with smaller elements. Example, you have a circle, and you want to represent it by using straight lines. Obviously, result will be closer to actual circle, if you use higher number of smaller sized lines.
REFER > www.colorado.edu/engineering/cas/courses.d/IFEM.d/IFEM.Ch01.d/IFEM.Ch01.pdf
and slide to Page 1-6. There are some visuals.
Mathematical > In finite difference, we get the solution on the grid points only. In Finite Element, we get the solution over the domain (i.e. at the nodes and anywhere in between). Now, unlike FDM, to get the solution on entire element, we use piecewise and well-behaved shape functions to interpolate from integration points. So, lets say you have a quadratic shape function and very large elements; while going from one node to another node, you might not be able to capture the whole transition. However, if you have smaller elements with same degreed shape functions, you will have a better representation. Lets say, axially loaded plate with a center hole on it. We know that there will be a stress gradient around the hole. We need to use an adaptivity or denser meshes in that area to get the better presentation. Or you can still use coarser mesh but then you should to use higher order polynomials for interpolation. These two called, h-method and p-method.
I hope it helps.