Multirate Technique for Explicit Discontinuous Galerkin Computations of Time-Domain Maxwell Equations on Complex Geometries

This paper presents a multirate technique to improve and optimize the time step of a second-order two-stage explicit Runge-Kutta (ERK) scheme. In this technique, the mesh elements are stored in different groups according to their stable time steps. These groups are sorted into two classes: 1) the bulk groups, where the two-stage ERK method is applied once or repeatedly; 2) the buffer groups that are used to accommodate the transition between two bulk groups. This technique is proposed for accelerating the explicit discontinuous Galerkin computations of the time-domain Maxwell equations. An application example on a human skull is proposed to show the efficiency of this technique and to simulate wave propagation on complex geometries.