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

Jichun Li Cengke Shi Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1804.25008

Computers and Mathematics with Applications, 73, 1760-1780, 2017
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.
Discontinuous Galerkin method, Maxwell's equations, metamaterials, leap-frog scheme
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@inproceedings{jichun2017optimal,
  title={Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials},
  author={Jichun Li, Cengke Shi, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416093756931765043},
  booktitle={Computers and Mathematics with Applications},
  volume={73},
  pages={1760-1780},
  year={2017},
}
Jichun Li, Cengke Shi, and Chi-Wang Shu. Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials. 2017. Vol. 73. In Computers and Mathematics with Applications. pp.1760-1780. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416093756931765043.
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