Volume 55, Number 5, September-October 2021
|Page(s)||2421 - 2443|
|Published online||26 October 2021|
Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems
Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P.R. China
2 Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea
3 School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P.R. China
4 NCMIS, LSEC and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China
5 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P.R. China
* Corresponding author: email@example.com
Accepted: 2 October 2021
In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the L2-norm and L∞-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (Wei et al. [SIAM J. Numer. Anal. 58 (2020) 1918–1940]).
Mathematics Subject Classification: 65N30 / 65N50 / 78A25
Key words: Well-posedness / stability / time-domain electromagnetic scattering / uniaxial PML / exponential convergence
© The authors. Published by EDP Sciences, SMAI 2021
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