Year: 2015
Author: Jiangxing Wang, Ziqing Xie, Chuanmiao Chen
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 6 : pp. 796–817
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 $\mathcal{O}(τ^2+h^{p+1/2})$. Numerical results in both 2D and 3D are provided to validate our theoretical prediction.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2014.m725
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 6 : pp. 796–817
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
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