Accurate 3D calculation of motion-induced eddy currents
The calculation of motion-induced eddy currents in massive conductors or permanent magnets yields a 3D convection-diffusion problem. Up-winding and SUPG formulations are well-established methods to obtain stable discretizations of the scalar convection-diffusion equations in the case of singular perturbation, but there is very little reported experience with the stability of convection in the vector case, i.e. in electromagnetism. We have introduced convection based concepts (SUPG, upwinding) in the context of electromagnetism and discussed their validity. The extrusion operator yields a geometrical upwind scheme without free parameter, in contrast to the SUPG scheme. The developed scheme is valid on simplicial meshes, and consistent and stable. It can however not be assembled element by element. In constrast to SUPG, information in the upwind element is required during assembly.