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A reduced-order discontinuous Galerkin method based on a Krylov subspace technique in nanophotonics

Author

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  • Li, Kun
  • Huang, Ting-Zhu
  • Li, Liang
  • Lanteri, Stéphane

Abstract

This paper is concerned with the design of a reduced-order model (ROM) based on a Krylov subspace technique for solving the time-domain Maxwell’s equations coupled to a Drude dispersion model, which are discretized in space by a discontinuous Galerkin (DG) method. An auxiliary differential equation (ADE) method is used to represent the constitutive relation for the dispersive medium. A semi-discrete DG scheme is formulated on an unstructured simplicial mesh, and is combined with a centered scheme for the definition of the numerical fluxes of the electric and magnetic fields on element interfaces. The ROM is established by projecting (Galerkin projection) the global semi-discrete DG scheme onto a low-dimensional Krylov subspace generated by an Arnoldi process. A low-storage Runge-Kutta (LSRK) time scheme is employed in the semi-discrete DG system and ROM. The overall goal is to reduce the computational time while maintaining an acceptable level of accuracy. We present numerical results on 2-D problems to show the effectiveness of the proposed method.

Suggested Citation

  • Li, Kun & Huang, Ting-Zhu & Li, Liang & Lanteri, Stéphane, 2019. "A reduced-order discontinuous Galerkin method based on a Krylov subspace technique in nanophotonics," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 128-145.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:128-145
    DOI: 10.1016/j.amc.2019.04.031
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    References listed on IDEAS

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    1. N. A. Mortensen & S. Raza & M. Wubs & T. Søndergaard & S. I. Bozhevolnyi, 2014. "A generalized non-local optical response theory for plasmonic nanostructures," Nature Communications, Nature, vol. 5(1), pages 1-7, September.
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