Research Article
Exponential convergence of Cartesian PML method for Maxwell’s equations in a two-layer medium
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 3, pp. 929-956.

The 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.

DOI : 10.1051/m2an/2019082
Classification : 35Q60, 65N30
Mots-clés : Cartesian perfectly matched layer, exponential convergence, electromagnetic scattering problem, Maxwell’s equation, two-layer medium 
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     author = {Duan, Xiaoqi and Jiang, Xue and Zheng, Weiying},
     title = {Exponential convergence of {Cartesian} {PML} method for {Maxwell{\textquoteright}s} equations in a two-layer medium},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {929--956},
     publisher = {EDP-Sciences},
     volume = {54},
     number = {3},
     year = {2020},
     doi = {10.1051/m2an/2019082},
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     zbl = {1437.35648},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2019082/}
}
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Duan, Xiaoqi; Jiang, Xue; Zheng, Weiying. Exponential convergence of Cartesian PML method for Maxwell’s equations in a two-layer medium. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 3, pp. 929-956. doi : 10.1051/m2an/2019082. http://www.numdam.org/articles/10.1051/m2an/2019082/

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