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Convergence of the PML method for elastic wave scattering problems


Authors: Zhiming Chen, Xueshuang Xiang and Xiaohui Zhang
Journal: Math. Comp. 85 (2016), 2687-2714
MSC (2010): Primary 65N30, 65N50
DOI: https://doi.org/10.1090/mcom/3100
Published electronically: March 22, 2016
MathSciNet review: 3522967
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Abstract: In this paper we study the convergence of the perfectly matched layer (PML) method for solving the time harmonic elastic wave scattering problems. We introduce a simple condition on the PML complex coordinate stretching function to guarantee the ellipticity of the PML operator. We also introduce a new boundary condition at the outer boundary of the PML layer which allows us to extend the reflection argument of Bramble and Pasciak to prove the stability of the PML problem in the truncated domain. The exponential convergence of the PML method in terms of the thickness of the PML layer and the strength of PML medium property is proved. Numerical results are included.


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Additional Information

Zhiming Chen
Affiliation: LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China.
Email: zmchen@lsec.cc.ac.cn

Xueshuang Xiang
Affiliation: Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China.
Email: xueshuangx@gmail.com

Xiaohui Zhang
Affiliation: LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China.
Email: zhangxh@lsec.cc.ac.cn

DOI: https://doi.org/10.1090/mcom/3100
Received by editor(s): June 23, 2014
Received by editor(s) in revised form: January 29, 2015, and June 28, 2015
Published electronically: March 22, 2016
Additional Notes: This work was supported in part by the National Basic Research Project under the grant 2011CB309700 and the China NSF under the grants 11021101 and 11321061.
Article copyright: © Copyright 2016 American Mathematical Society

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