Homology and Cohomology Computation in Finite Element Modeling

A homology and cohomology solver for finite element meshes is represented. It is an integrated part of the finite element mesh generator Gmsh. We demonstrate the exploitation of the cohomology computation results in a finite element solver, and use an induction heating problem as a working example. The homology and cohomology solver makes the use of a vectorscalar potential formulation straightforward. This gives better overall performance than a vector potential formulation. Cohomology computation also clarifies the lumped parameter coupling of the problem and enables the user to obtain useful post-processing data as a part of the finite element solution.