A Numerical Solution for the Time Variant Maxwell Equations using a Discontinuous Galerkin Method

Abstract

In this work a parallel scheme to solve the dynamic Maxwell’s equations is presented, in order to simulate an electromagnetic wave in a two-dimensional domain composed of distinct dielectric materials and subject to boundary conditions. In this approach a Discontinuous Galerkin Finite Element Method (DG-FEM) is used to compute the solution over a discretized domain of non-overlapping straight-sided elements. In contrast to continuous Galerkin methods, the core of the simulation relies on a set of elementwise calculations instead of a global processing. These local calculations are computed simultaneously in a shared memory environment with the parallel framework proposed, taking advantage of the discontinuous nature of the solver implemented.