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

Kun Li 1 Ting-Zhu Huang 2 Liang Li 3 Stéphane Lanteri 3
1 UESTC - University of Electronic Science and Technology of China
2 UESTC - School of Mathematical Sciences [Chengdu]
3 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
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.
Keywords : Discontinuous Galerkin method Reduced-order model Krylov subspace technique Arnoldi process Nanophotonics
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Journal articles
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https://hal.inria.fr/hal-02433050
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Submitted on : Wednesday, January 8, 2020 - 6:57:11 PM
Last modification on : Friday, January 21, 2022 - 11:13:11 AM

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Kun Li, Ting-Zhu Huang, Liang Li, Stéphane Lanteri. A reduced-order discontinuous Galerkin method based on a Krylov subspace technique in nanophotonics. Applied Mathematics and Computation, Elsevier, 2019, 358, pp.128-145. ⟨10.1016/j.amc.2019.04.031⟩. ⟨hal-02433050⟩

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