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Exponential convergence of Cartesian PML method for Maxwell's equations in a two-layer medium
Duan, Xiaoqi1,2; Jiang, Xue3; Zheng, Weiying1,4
2020-04-09
Source PublicationESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN0764-583X
Volume54Issue:3Pages:929-956
AbstractThe perfectly matched layer (PML) method is extensively studied for scattering problems in homogeneous background media. However, rigorous studies on the PML method in layered media are very rare in the literature, particularly, for three-dimensional electromagnetic scattering problems. Cartesian PML method is favorable in numerical solutions since it is apt to deal with anisotropic scatterers and to construct finite element meshes. Its theories are more difficult than circular PML method due to anisotropic wave-absorbing materials. This paper presents a systematic study on the Cartesian PML method for three-dimensional electromagnetic scattering problem in a two-layer medium. We prove the well-posedness of the PML truncated problem and that the PML solution converges exponentially to the exact solution as either the material parameter or the thickness of PML increases. To the best of the authors' knowledge, this is the first theoretical work on Cartesian PML method for Maxwell's equations in layered media.
KeywordCartesian perfectly matched layer exponential convergence electromagnetic scattering problem Maxwell's equation two-layer medium
DOI10.1051/m2an/2019082
Indexed BySCI
Language英语
Funding ProjectNational Science Fund for Distinguished Young Scholars[11725106] ; China NSF[11831016] ; China NSF[11771057] ; China NSF[11671052]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000526853400001
PublisherEDP SCIENCES S A
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51197
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZheng, Weiying
Affiliation1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
3.Beijing Univ Technol, Coll Appl Sci, Beijing, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSEC, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Duan, Xiaoqi,Jiang, Xue,Zheng, Weiying. Exponential convergence of Cartesian PML method for Maxwell's equations in a two-layer medium[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2020,54(3):929-956.
APA Duan, Xiaoqi,Jiang, Xue,&Zheng, Weiying.(2020).Exponential convergence of Cartesian PML method for Maxwell's equations in a two-layer medium.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,54(3),929-956.
MLA Duan, Xiaoqi,et al."Exponential convergence of Cartesian PML method for Maxwell's equations in a two-layer medium".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 54.3(2020):929-956.
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