Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials
Computers and Mathematics with Applications
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Simulation of electromagnetic wave propagation in metamaterials leads to more complicated time domain Maxwell's equations than the standard Maxwell's equations in free space. In this paper, we develop and analyze a non-dissipative discontinuous Galerkin (DG) method for solving the Maxwell's equations in Drude metamaterials. Previous discontinuous Galerkin methods in the literature for electromagnetic wave propagation in metamaterials were either non-dissipative but sub-optimal, or dissipative and optimal. Our method uses a different and simple choice of numerical fluxes, achieving provable non-dissipative stability and optimal error estimates simultaneously. We prove the stability and optimal error estimates for both semi- and fully discrete DG schemes, with the leap-frog time discretization for the fully discrete case. Numerical results are given to demonstrate that the DG method can solve metamaterial Maxwell's equations effectively. © 2017 Elsevier Ltd
Shu, C. W.
Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials.
Computers and Mathematics with Applications, 73(8),