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

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.