DGTD method on hybrid meshes for time domain electromagnetics

Abstract

This paper is concerned with a preliminary investigation of a Discontinuous Galerkin Time Domain (DGTD) method formulated on hybrid quadrangular-triangular meshes for the solution of the two-dimensional Maxwell equations. The general objective of this study is to enhance the flexibility and the efficiency of DGTD methods for large-scale time domain electromagnetic wave propagation problems with regards to the discretization process of complex propagation scenes and the work discussed here is a first step in this direction. Within each mesh element, the electromagnetic field components are approximated by a high order nodal polynomial and time integration of the associated semi-discrete equations is achieved by a second order Leap-Frog scheme. We study the stability of the resulting DGTD method and present numerical results aiming at the validation of the method on a model problem.