Anisotropic Mesh Adaptation Based on Error Estimation for 3D Finite Element Simulation of Electromagnetic Material Processing

This work aims to develop an adaptive remeshing procedure for finite element method on electromagnetic computations. A thorough comparison of metric computation strategies is carried out as it constitutes a cornerstone of this developments. This procedure will focus on the mesh size adaptation to distribute the error uniformly over a computational domain, in order to obtain a user-prescribed accuracy of the solution. Also, it shall enable dealing with complex geometries for electromagnetic-coupled material processing applications. For this purpose, a quasi-steady state approximation of the Maxwell's equations in a time-domain formalism is considered. The automatic remeshing procedure is based on the following key steps: An a posteriori error estimator to pinpoint the critical areas needing refinement or allowing coarsening. An anisotropic metric approximation. Both steps use a global field recovery algorithm in order to enable robust gradient computation. Finally, several 3D test cases are presented.