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Solving Maxwell's Equation in Meta-Materials by a CG-DG Method

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  17 May 2016

Ziqing Xie ,
Jiangxing Wang ,
Bo Wang  and
Chuanmiao Chen
Ziqing Xie*
Affiliation:
Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China
Jiangxing Wang*
Affiliation:
Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China Beijing Computational Science Research Center, Beijing 100094, China
Bo Wang*
Affiliation:
Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China
Chuanmiao Chen*
Affiliation:
Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China
*
*Corresponding author. Email addresses:ziqingxie@foxmail.com (Z. Xie), wangjianghai3871@163.com (J. Wang), bowanghn@gmail.com (B. Wang), cmchen@hunnu.edu.cn (C. Chen)
*Corresponding author. Email addresses:ziqingxie@foxmail.com (Z. Xie), wangjianghai3871@163.com (J. Wang), bowanghn@gmail.com (B. Wang), cmchen@hunnu.edu.cn (C. Chen)
*Corresponding author. Email addresses:ziqingxie@foxmail.com (Z. Xie), wangjianghai3871@163.com (J. Wang), bowanghn@gmail.com (B. Wang), cmchen@hunnu.edu.cn (C. Chen)
*Corresponding author. Email addresses:ziqingxie@foxmail.com (Z. Xie), wangjianghai3871@163.com (J. Wang), bowanghn@gmail.com (B. Wang), cmchen@hunnu.edu.cn (C. Chen)

Abstract

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In this paper, an approach combining the DG method in space with CG method in time (CG-DG method) is developed to solve time-dependent Maxwell's equations when meta-materials are involved. Both the unconditional L2-stability and error estimate of order are obtained when polynomials of degree at most r is used for the temporal discretization and at most k for the spatial discretization. Numerical results in 3D are given to validate the theoretical results.

Keywords

Maxwell's equationsmeta-materialsfull-discretizationCG-DG methodL2-stabilityL2-error estimate

MSC classification

Secondary: 35Q61: Maxwell equations 65M12: Stability and convergence of numerical methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1242 - 1264
Copyright
Copyright © Global-Science Press 2016 

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