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

被引：11

作者：

Wang, Jiangxing ^{[1
]}

Xie, Ziqing ^{[1
]}

Chen, Chuanmiao ^{[1
]}

机构：

[1] Hunan Normal Univ, Coll Math & Comp Sci, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2015年 / 7卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Maxwell's equations; metamaterials; fully disctete; DG method; L-2-stability; L-2-error estimate; DISCONTINUOUS GALERKIN METHOD; DISPERSIVE MEDIA; WAVE-PROPAGATION; CONVERGENCE;

D O I：

10.4208/aamm.2014.m725

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 (tau(2) + h(p+1/2)). Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

引用

页码：796 / 817

页数：22

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