Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials

Document Type

Article

Publication Date

1-1-2017

Publication Title

Computers and Mathematics with Applications

Volume

73

Issue

8

First page number:

1760

Last page number:

1780

Abstract

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

Language

english

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