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Boundary condition for weak PDE form
Posted Mar 1, 2012, 10:17 a.m. EST Studies & Solvers Version 3.5a 3 Replies
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I've been doing some simulation coupling RF and PDE (weak form) application modes. There are something about boundary condition in weak form confusing me.
As said in documentation, boundary conditions are automatically included in weak form when they are utilized to cancel surface integrals. Therefore there's no need to enforce them explicitly as boundary conditions or constraint. However, I find it is not true. COMSOL can give some solution, but it's easy to see that the boundary conditions are not fulfilled by checking postprocessing results. If the boundary conditions are enforced, I get reasonable results.
On the other hand, when I enforce all boundary conditions explicitly, sometimes errors occur during solving, saying something like "not convergent". It seems to me the equation system is overdetermined, so that no solution is found. (Is it right to think this way?)
Above all, I'm confused by these inconsistent observations...
Anybody knows about this issue? Thanks!
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When all boundary conditions are enforced, the result (not convergent) looks physically reasonable except singularly large values occur at some points around boundaries. The boundary conditions are consistent, at least in the sense of physics, I guess thus the solution looks correct. However, I have no idea where those singular points come from.
Thanks!
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it would be easier for us to follow you if we had a model too look at ;)
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Good luck
Ivar
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Thanks for your reply!
Attached is the model. But it's not easy to describe what I'm doing in the model. I will try to explain it.
The circular region in the model is divided into two parts. The upper part is modeled by non-vacuum permittivity in RF module. Physically, the lower part is the same material. However, as kinda of numerical experiment, I want to numerically realize the material property by coupling the vacuum Maxwell's equations with a PDE. In principle, both ways are equivalent. The tricky thing is the interface between the two semi-circles.
In the attached model file, Dirichlet boundary conditions are explicitly imposed as constraints on the interface. The result is basically the same as that when I model both regions with the permittivity. You can see extremely large field appears along the interface.
On the other hand, if no constraints are imposed on the interface, the result is almost perfect.
I suddenly realize you don't have v3.5a on your pc right after I wrote the above description... Anyway I upload the model file. See below for the download link. Maybe the file is too big to upload here.
ifile.it/6cptq21/Modelfile.mph