Dissipative Scheme for Discontinuous Galerkin Time-Domain Method Based on a Leap-Frog Time-Stepping
Keywords:
Backward discretization, centered fluxes, dissipative scheme, discontinuous Galerkin, fully explicit time-stepping, Fourier analysis, periodic boundary conditionsAbstract
A dissipative scheme is proposed to improve numerical dispersion and eliminate spurious modes in the unstructured grid-based discontinuous Galerkin time-domain (DGTD) method. We introduce the dissipative terms into the centered fluxes, and a backward discretization in time is applied to the dissipative part to yield a fully explicit time-stepping scheme. In order to analyze the dispersion and dissipation properties of this scheme, we perform a numerical Fourier analysis to the normalized one-dimensional Maxwell’s equations with periodic boundary conditions. In this process, the mechanism of suppression of the spurious modes is revealed for the dissipative scheme. Numerical results show that more accurate solutions can be obtained by using dissipative scheme in the DG method.
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References
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