Volume 7, Issue 6
Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials

Jiangxing Wang, Ziqing Xie & Chuanmiao Chen

Adv. Appl. Math. Mech., 7 (2015), pp. 796-817.

Published online: 2018-05

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  • Abstract

An implicit discontinuous Galerkin method is introduced to solve the timedomain 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(τ 2+h p+1/2). Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

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@Article{AAMM-7-796, author = {Jiangxing Wang, Ziqing Xie and Chuanmiao Chen}, title = {Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {6}, pages = {796--817}, abstract = {

An implicit discontinuous Galerkin method is introduced to solve the timedomain 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(τ 2+h p+1/2). Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m725}, url = {http://global-sci.org/intro/article_detail/aamm/12240.html} }
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