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Stable and unstable solutions
Posted Nov 17, 2011, 10:39 a.m. EST Modeling Tools & Definitions, Parameters, Variables, & Functions 5 Replies
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I have a quick question about the new features in Comsol (4.0 or higher), in particular, the option "Continuation" in the "Extension" submenu of a stationary study does it mean that it performs an Arc-Length path-following? That is that it can follow both stable and unstable equilibrium branches?
Because, I'm implementing a nonlinear model already used in Comsol 3.5 and I obtained the same results also with comsol 4.2, that is, when the tangent stiffness matrix becomes singular, the code stop the simulation.
Thank-you
Andrea
Because, I'm implementing a nonlinear model already used in Comsol 3.5 and I obtained the same results also with comsol 4.2, that is, when the tangent stiffness matrix becomes singular, the code stop the simulation.
Thank-you
Andrea
5 Replies Last Post Nov 18, 2011, 3:37 p.m. EST
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Posted:
1 decade ago
Hi
continuation is a parametric sweep, but one looping around the solver alone, hence not changing the geometry or the mesh. Typically the extension sweep uses the result from the previous solving process as initial conditions for the next one.
You have the outer "Parametric" sweep which applies from its node position to the end of the node branch, which also loops around the geometry and the mesh, hence if you have a parameter that changes the geometry it will adapt the geometry (provided you do not change the overall topology, i.e.not creating new domains or boundaries) then it would remesh and then solve, but always with the initial conditions you have specified in the physics solver sequence. This is quite different from the "continuation" sweep
Working with bifurcations is tricky, you might indeed use a continuation sweep to guide COMSOL towards one solution, but that I have never really tried. Pls report back if you have some good , or bad experiences with this, always useful to know
--
Good luck
Ivar
continuation is a parametric sweep, but one looping around the solver alone, hence not changing the geometry or the mesh. Typically the extension sweep uses the result from the previous solving process as initial conditions for the next one.
You have the outer "Parametric" sweep which applies from its node position to the end of the node branch, which also loops around the geometry and the mesh, hence if you have a parameter that changes the geometry it will adapt the geometry (provided you do not change the overall topology, i.e.not creating new domains or boundaries) then it would remesh and then solve, but always with the initial conditions you have specified in the physics solver sequence. This is quite different from the "continuation" sweep
Working with bifurcations is tricky, you might indeed use a continuation sweep to guide COMSOL towards one solution, but that I have never really tried. Pls report back if you have some good , or bad experiences with this, always useful to know
--
Good luck
Ivar
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Posted:
1 decade ago
Hi Mr Kjelberg,
thank you for your quick reply.
I want to specify that in my continuation, no geometry or mesh are varying.
I use PDE mode, to perform static and dynamic nonlinear analyses on my analytical models. I was just curious about this, let me say now "renamed", parametric tool of comsol 4.x
I asked for this because in a workshop here in Rome, I asked for that, precisely about the capability of new comsol to path follow unstable branches of equilibrium solutions...and the guy that was talking for comsol in this workshop ensured me that "continuation" did mean exactly that in new Comsol....I had many doubts about that and now these doubts are confirmed.
Thank-you again
Andrea
thank you for your quick reply.
I want to specify that in my continuation, no geometry or mesh are varying.
I use PDE mode, to perform static and dynamic nonlinear analyses on my analytical models. I was just curious about this, let me say now "renamed", parametric tool of comsol 4.x
I asked for this because in a workshop here in Rome, I asked for that, precisely about the capability of new comsol to path follow unstable branches of equilibrium solutions...and the guy that was talking for comsol in this workshop ensured me that "continuation" did mean exactly that in new Comsol....I had many doubts about that and now these doubts are confirmed.
Thank-you again
Andrea
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Posted:
1 decade ago
Hi
if you have bifurcations, you need to tell COMSOL some-way which path to choose, COMSOL cannot choose for you alone, neither take both paths (except, I have noticed that if you work directly in PDE and do not give enough BC, you might end up with 2 stable solutions, and COMSOL will oscillate between both, then visually you will see the two solutions if you connect the result points differently, but you cannot do any maths on such noisy results), then indeed the only way is to use the continuation sweep + something else, it's just that "how to define the something else ?
--
Good luck
Ivar
if you have bifurcations, you need to tell COMSOL some-way which path to choose, COMSOL cannot choose for you alone, neither take both paths (except, I have noticed that if you work directly in PDE and do not give enough BC, you might end up with 2 stable solutions, and COMSOL will oscillate between both, then visually you will see the two solutions if you connect the result points differently, but you cannot do any maths on such noisy results), then indeed the only way is to use the continuation sweep + something else, it's just that "how to define the something else ?
--
Good luck
Ivar
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Posted:
1 decade ago
I'm sorry, I don't understand, so does comsol have an arc-length algorithm implemented?
If has it, well it can path-follow also the unstable branches if not it can't.
If has it, well it can path-follow also the unstable branches if not it can't.
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Posted:
1 decade ago
Hi
I'm not familiar enough with that domain of simulations, the best is to ask "support" directly. But as you can almost add whatever you want to COMSOL, either within the GUI or via matlab I'm rather sure there are ways around, but it might not be implemented pre-cooked as you need it, today (I'm not COMSOL, just a user, but rather fan of the tool ;)
--
Good luck
Ivar
I'm not familiar enough with that domain of simulations, the best is to ask "support" directly. But as you can almost add whatever you want to COMSOL, either within the GUI or via matlab I'm rather sure there are ways around, but it might not be implemented pre-cooked as you need it, today (I'm not COMSOL, just a user, but rather fan of the tool ;)
--
Good luck
Ivar