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Volume 19, Issue 5
Solving Maxwell's Equation in Meta-Materials by a CG-DG Method

Ziqing Xie, Jiangxing Wang, Bo Wang & Chuanmiao Chen

DOI: 10.4208/cicp.scpde14.35s

Commun. Comput. Phys., 19 (2016), pp. 1242-1264.

Published online: 2018-04

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  • Abstract

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 $L^2$-stability and error estimate of order $\mathcal{O}$($τ^ {r+1}$+$h^{k+\frac{1}{2}}$) 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.

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@Article{CiCP-19-1242, author = {Ziqing Xie, Jiangxing Wang, Bo Wang and Chuanmiao Chen}, title = {Solving Maxwell's Equation in Meta-Materials by a CG-DG Method}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {5}, pages = {1242--1264}, abstract = {

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 $L^2$-stability and error estimate of order $\mathcal{O}$($τ^ {r+1}$+$h^{k+\frac{1}{2}}$) 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.35s}, url = {http://global-sci.org/intro/article_detail/cicp/11127.html} }
TY - JOUR T1 - Solving Maxwell's Equation in Meta-Materials by a CG-DG Method AU - Ziqing Xie, Jiangxing Wang, Bo Wang & Chuanmiao Chen JO - Communications in Computational Physics VL - 5 SP - 1242 EP - 1264 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.scpde14.35s UR - https://global-sci.org/intro/article_detail/cicp/11127.html KW - AB -

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 $L^2$-stability and error estimate of order $\mathcal{O}$($τ^ {r+1}$+$h^{k+\frac{1}{2}}$) 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.

Ziqing Xie, Jiangxing Wang, Bo Wang and Chuanmiao Chen. (2018). Solving Maxwell's Equation in Meta-Materials by a CG-DG Method. Communications in Computational Physics. 19 (5). 1242-1264. doi:10.4208/cicp.scpde14.35s
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