An Unconditionally Stable Discontinuous Galerkin Method for Solving the 2-D Time-Domain Maxwell Equations on Unstructured Triangular Meshes

Abstract

Numerical methods for solving the time-domain Maxwell equations often rely on Cartesian meshes and are variants of the finite-difference time-domain (FDTD) method due to Yee (1966). In recent years, there has been an increasing interest in discontinuous Galerkin time-domain (DGTD) methods dealing with unstructured meshes since the latter are particularly well adapted to the discretization of geometrical details that characterize applications of practical relevance. However, similarly to Yee's finite difference time-domain method, existing DGTD methods generally rely on explicit time integration schemes and are therefore constrained by a stability condition that can be very restrictive on locally refined unstructured meshes. An implicit time integration scheme is a possible strategy to overcome this limitation. The present study aims at investigating such an implicit DGTD method for solving the 2-D time-domain Maxwell equations on nonuniform triangular meshes.