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Convergence of an Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems

Part of:Basic linear algebraNumerical linear algebra

Published online by Cambridge University Press:  20 July 2016

Chao Liang and
Xueshuang Xiang
Chao Liang*
Affiliation:
Science and Technology on Electronic Information Control Laboratory, Chengdu 610036, ChinaLSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Xueshuang Xiang*
Affiliation:
Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China
*
*Corresponding author. Email addresses:liangchao@lsec.cc.ac.cn (C. Liang), xiangxueshuang@qxslab.cn (X. S. Xiang)
*Corresponding author. Email addresses:liangchao@lsec.cc.ac.cn (C. Liang), xiangxueshuang@qxslab.cn (X. S. Xiang)

Abstract

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The anisotropic perfectly matched layer (APML) defines a continuous vector field outside a rectangle domain and performs the complex coordinate stretching along the vector field. Inspired by [Z. Chen et al., Inverse Probl. Imag., 7, (2013):663–678] and based on the idea of the shortest distance, we propose a new approach to construct the vector field which still allows us to prove the exponential decay of the stretched Green function without the constraint on the thickness of the PML layer. Moreover, by using the reflection argument, we prove the stability of the PML problem in the PML layer and the convergence of the PML method. Numerical experiments are also included.

Keywords

Anisotropic PMLHelmholtz equationReflection argumentExponential convergence

MSC classification

Secondary:15A12: Conditioning of matrices65F10: Iterative methods for linear systems65F15: Eigenvalues, eigenvectors

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 3 , August 2016, pp. 358 - 382
Copyright
Copyright © Global-Science Press 2016 

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