|Magneto-thermal model of an induction heating device using cohomology conditions|
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To run the models, open
indheat.pro with Gmsh.
The example contains a 3D model of an induction heating device, using T-Omega and A-v formulations and the Gmsh cohomology solver. It also includes simple thermal coupling.
The electromagnetic modeling aspects of the problem turn out to be subtle. The so-called A-V formulation of the problem is straightforward to implement, but it results in a large linear system that might be difficult to solve. In the T−Omega formulation of the problem, the same accuracy is achieved with a smaller linear system, but its implementation involves so-called thick-cuts, or source fields, that aren't discussed much in the finite element curriculum and may be difficult to produce. Here, we call them cohomology basis functions, and generate them using the cohomology solver implemented in Gmsh. See  for the details.
- M. Pellikka, S. Suuriniemi, L. Kettunen and C. Geuzaine. Homology and Cohomology Computation in Finite Element Modeling. SIAM Journal on Scientific Computing 35 (5), B1195-B1214, 2013.
Models developed by M. Pellikka, S. Suuriniemi, L. Kettunen and @geuzaine.