Causal-Path Local Time-Stepping in the discontinuous Galerkin method for Maxwellʼs equations

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 Leap-Frog (LF2). The CPLTS method is applied to evolve Maxwellʼs 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 Montsenyʼs LF2 technique. The results show that the CPLTS technique improves the dispersive and dissipative properties of LF2-LTS scheme.