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

被引：2

作者：

Li, Kun ^{[1
]}

Huang, Ting-Zhu ^{[1
]}

Li, Liang ^{[1
]}

Lanteri, Stephane ^{[2
]}

机构：

[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China

[2] INRIA, 2004 Route Lucioles,BP 93, F-06902 Sophia Antipolis, France

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 358卷

关键词：

Discontinuous Galerkin method; Reduced-order model; Krylov subspace technique; Arnoldi process; Nanophotonics; MAXWELLS EQUATIONS; PADE-APPROXIMATION; MODEL-REDUCTION; SYSTEMS; SIMULATION;

D O I：

10.1016/j.amc.2019.04.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：128 / 145

页数：18