An adaptive edge finite element method for the Maxwell's equations in metamaterials

Hao Wang; Wei Yang; Yunqing Huang; Hao Wang; Wei Yang; Yunqing Huang

doi:10.3934/era.2020051

Electronic Research Archive

2020, Volume 28, Issue 2: 961-976. doi: 10.3934/era.2020051

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An adaptive edge finite element method for the Maxwell's equations in metamaterials

Hao Wang ^{1
,},
Wei Yang ^{1
,},
Yunqing Huang ^{2
,}

1.
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China
2.
Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China

Received: 01 February 2020 Revised: 01 April 2020
78M10, 65N30

In this paper, we study an adaptive edge finite element method for time-harmonic Maxwell's equations in metamaterials. A-posteriori error estimators based on the recovery type and residual type are proposed, respectively. Based on our a-posteriori error estimators, the adaptive edge finite element method is designed and applied to simulate the backward wave propagation, electromagnetic splitter, rotator, concentrator and cloak devices. Numerical examples are presented to illustrate the reliability and efficiency of the proposed a-posteriori error estimations for the adaptive method.
- Maxwell's equations,
- wave source terms,
- a-posteriori error estimator,
- adaptive edge finite element method,
- metamaterial media
Citation: Hao Wang, Wei Yang, Yunqing Huang. An adaptive edge finite element method for the Maxwell's equations in metamaterials[J]. Electronic Research Archive, 2020, 28(2): 961-976. doi: 10.3934/era.2020051

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Abstract

In this paper, we study an adaptive edge finite element method for time-harmonic Maxwell's equations in metamaterials. A-posteriori error estimators based on the recovery type and residual type are proposed, respectively. Based on our a-posteriori error estimators, the adaptive edge finite element method is designed and applied to simulate the backward wave propagation, electromagnetic splitter, rotator, concentrator and cloak devices. Numerical examples are presented to illustrate the reliability and efficiency of the proposed a-posteriori error estimations for the adaptive method.

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