Causal-Path Local Time-Stepping in the Discontinuous Galerkin Method for Maxwell’s equations

Abstract

We introduce a novel local time-stepping technique for marching-in-time algorithms. The technique is denoted as Causal-Path Local Time-Stepping (CPLTS) and it is ap- plied for two time integration techniques: fourth order low{storage explicit Runge{Kutta (LSERK4) and second order Leapfrog (LF2). The CPLTS method is applied to evolve Maxwell's curl equations using a Discontinuous Galerkin (DG) scheme for the spatial discretization. Numerical results for LF2 and LSERK4 are compared with analytical so- lutions and the Montseny's LF2 technique. The results show that the CPLTS technique improves the dispersive and dissipative properties of LF2-LTS scheme.