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Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials

Published online by Cambridge University Press:  09 September 2015

Jiangxing Wang ,
Ziqing Xie  and
Chuanmiao Chen
Jiangxing Wang
Affiliation:
Key Laboratory of High Performance Computing and Stochastic Information Processing, College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
Ziqing Xie*
Affiliation:
Key Laboratory of High Performance Computing and Stochastic Information Processing, College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
Chuanmiao Chen
Affiliation:
Key Laboratory of High Performance Computing and Stochastic Information Processing, College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
*
*Corresponding author. Email: wangjianghai3871@163.com (J. X. Wang), zqxie01@hotmail.com (Z. Q. Xie), cmchen@hunnu.edu.cn
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Abstract

An implicit discontinuous Galerkin method is introduced to solve the time-domain Maxwell’s equations in metamaterials. The Maxwell’s equations in metamaterials are represented by integral-differential equations. Our scheme is based on discontinuous Galerkin method in spatial domain and Crank-Nicolson method in temporal domain. The fully discrete numerical scheme is proved to be unconditionally stable. When polynomial of degree at most p is used for spatial approximation, our scheme is verified to converge at a rate of O(τ2+hp+1/2). Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

Keywords

65M1265M60Maxwell’s equationsmetamaterialsfully discteteDG method, L2-stabilityL2-error estimate

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Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 6 , December 2015 , pp. 796 - 817
Copyright
Copyright © Global-Science Press 2015 

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