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

This work aims to develop an adaptive remeshing procedure for the finite-element method (FEM) on electromagnetic computations. A thorough comparison of metric computation strategies is carried out as it constitutes a cornerstone of this development. This procedure will focus on the mesh size adaptation to distribute the error uniformly over a computational domain, to achieve a user-prescribed solution accuracy. Also, it shall enable dealing with complex geometries for electromagnetic-coupled material processing applications. For this purpose, a quasi-steady-state approximation of 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 to enable robust gradient computation. Finally, several 3-D test cases are presented.