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

TL;DR

This paper presents CPLTS, a new local time-stepping method for Maxwell's equations using DG schemes, enhancing stability and accuracy of explicit time integration methods like LF2 and LSERK4.

Contribution

The paper introduces CPLTS, a novel local time-stepping approach for Maxwell's equations with DG discretization, applicable to multiple explicit time integration schemes.

Findings

CPLTS improves dispersive properties of LF2-LTS scheme.

CPLTS reduces dissipation in the numerical solution.

Numerical results validate enhanced accuracy and stability.

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 applied 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 solutions and the Montseny's LF2 technique. The results show that the CPLTS technique improves the dispersive and dissipative properties of LF2-LTS scheme.