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Causal-path local time-stepping in the discontinuous Galerkin method for Maxwell’s equations. (English) Zbl 1349.78061

Summary: 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 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.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
78A25 Electromagnetic theory (general)
78A40 Waves and radiation in optics and electromagnetic theory
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