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Inverse Problems and Imaging (IPI)
 

An anisotropic perfectly matched layer method for Helmholtz scattering problems with discontinuous wave number

Pages: 663 - 678, Volume 7, Issue 3, August 2013      doi:10.3934/ipi.2013.7.663

 
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Zhiming Chen - LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (email)
Chao Liang - LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (email)
Xueshuang Xiang - LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (email)

Abstract: The anisotropic perfectly matched layer (PML) defines a continuous vector field outside a rectangle domain and performs the complex coordinate stretching along the direction of the vector field. In this paper we propose a new way of constructing the vector field which allows us to prove the exponential decay of the stretched Green function without the constraint on the thickness of the PML layer. We report numerical experiments to illustrate the competitive behavior of the proposed PML method.

Keywords:  Helmholtz equation, discontinuous wave number, anisotropic PML.
Mathematics Subject Classification:  Primary: 65N30; Secondary: 78A45, 35Q60.

Received: September 2012;      Revised: February 2013;      Available Online: September 2013.

 References