AN ADAPTIVE EDGE FINITE ELEMENT METHOD FOR THE MAXWELL'S EQUATIONS IN METAMATERIALS

被引：6

作者：

Wang, Hao ^{[1
]}

Yang, Wei ^{[1
]}

Huang, Yunqing ^{[2
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Minist Educ, Key Lab Intelligent Comp & Informat Proc, Xiangtan 411105, Hunan, Peoples R China

来源：

ELECTRONIC RESEARCH ARCHIVE | 2020年 / 28卷 / 02期

关键词：

Maxwell's equations; wave source terms; a-posteriori error estimator; adaptive edge finite element method; metamaterial media; QUASI-STATIC APPROXIMATION; ERROR ESTIMATORS; WAVE-PROPAGATION; RECOVERY; CLOAKING; SCATTERING; RESONANCE; FULL;

D O I：

10.3934/era.2020051

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：961 / 976

页数：16

共 50 条

[21] An Adaptive Finite Element Method for Two-Dimensional Transverse Magnetic Time Harmonic Maxwell's Equations with General Material Properties and General Boundary Conditions [J].

Brenner, S. C. ;

Gedicke, J. ;

Sung, L. -Y. .

JOURNAL OF SCIENTIFIC COMPUTING, 2016, 68 (02) :848-863

[22] Implicit DG Method for Time Domain Maxwell's Equations Involving Metamaterials [J].

Wang, Jiangxing ;

Xie, Ziqing ;

Chen, Chuanmiao .

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2015, 7 (06) :796-817

[23] Huygens' surface excitation for the finite element method applied to Maxwell's equations-A construction based on Nitsche's method [J].

Winges, Johan ;

Rylander, Thomas .

JOURNAL OF COMPUTATIONAL PHYSICS, 2023, 488

[24] Adaptive hp-Finite Element Computations for Time-Harmonic Maxwell's Equations [J].

Jiang, Xue ;

Zhang, Linbo ;

Zheng, Weiying .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2013, 13 (02) :559-582

[25] A Second Order Nonconforming Rectangular Finite Element Method for Approximating Maxwell's Equations [J].

Dong-yang SHI 1 .

Acta Mathematicae Applicatae Sinica, 2011, 27 (04) :739-748

[26] Proposal of finite element analysis method for dielectric breakdown based on Maxwell's equations [J].

Noguchi, Satosh ;

Nakamichi, Misumi ;

Oguni, Kenji .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2020, 371

[27] A second order nonconforming rectangular finite element method for approximating Maxwell's equations [J].

Shi, Dong-yang ;

Hao, Xiao-bin .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2011, 27 (04) :739-748

[28] A second order nonconforming rectangular finite element method for approximating Maxwell’s equations [J].

Dong-yang Shi ;

Xiao-bin Hao .

Acta Mathematicae Applicatae Sinica, English Series, 2011, 27 :739-748

[29] A Fully Fourth Order Accurate Energy Stable Finite Difference Method for Maxwell's Equations in Metamaterials [J].

Sakkaplangkul, Puttha ;

Bokil, Vrushali A. ;

Carvalho, Camille .

IEEE JOURNAL ON MULTISCALE AND MULTIPHYSICS COMPUTATIONAL TECHNIQUES, 2019, 4 :260-268

[30] An hp-adaptive finite element method for electromagnetics.: Part 3:: A three-dimensional infinite element for Maxwell's equations [J].

Cecot, W ;

Rachowicz, W ;

Demkowicz, L .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2003, 57 (07) :899-921

← 1 2 3 4 5 →