Implicit discontinuous Galerkin methods for solving the time domain Maxwell equations on unstructured triangular meshes

摘要

Numerical methods for solving the time domain Maxwell equations most often rely on cartesian meshes and are variants of the finite difference time domain method originating in the seminal work of Yee [1]. However, in the recent years, there has been an increasing interest in discontinuous Galerkin time domain methods dealing with unstructured meshes since the latter are particularly well suited for the discretization of geometrical details that characterize applications of practical relevance. Similarly to Yee's finite difference time domain method, discontinuous Galerkin time domain methods generally rely on explicit time integration schemes and are therefore constrained by a stability condition that can be very restrictive on highly refined or unstructured meshes. An implicit time integration scheme is a natural way to obtain a time domain method which is unconditionally stable. The present study aims at investigating the applicability of an implicit time integration scheme in conjunction with a discontinuous Galerkin approximation method for solving the time domain Maxwell equations on unstructured triangular meshes.