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

Published: 01 October 2019 Publication History

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.

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          Published In

          cover image Applied Mathematics and Computation
          Applied Mathematics and Computation  Volume 358, Issue C
          Oct 2019
          491 pages

          Publisher

          Elsevier Science Inc.

          United States

          Publication History

          Published: 01 October 2019

          Author Tags

          1. Discontinuous Galerkin method
          2. Reduced-order model
          3. Krylov subspace technique
          4. Arnoldi process
          5. Nanophotonics

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