Convergence of the PML method for elastic wave scattering problems

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 n...

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Bibliographic Details
Published in:	Mathematics of computation Vol. 85; no. 302; pp. 2687 - 2714
Main Authors:	Chen, Zhiming, Xiang, Xueshuang, Zhang, Xiaohui
Format:	Journal Article
Language:	English
Published:	American Mathematical Society 01-11-2016
Online Access:	Get full text
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Summary:	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.
ISSN:	0025-5718 1088-6842
DOI:	10.1090/mcom/3100