Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 73, Issue 8, Pages 1760-1780Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2017.02.018
Keywords
Discontinuous Galerkin method; Maxwell's equations; Metamaterials; Leap-frog scheme
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Funding
- Simons Foundation [281296]
- NSF [DMS-1416742, DMS-1418750]
- DOE [DE-FG02-08ER25863]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1418750, 1416742] Funding Source: National Science Foundation
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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. (C) 2017 Elsevier Ltd. All rights reserved.
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