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Volume 9, Issue 3
Convergence of an Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems

Chao Liang & Xueshuang Xiang

DOI: 10.4208/nmtma.2016.m1505

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 358-382.

Published online: 2016-09

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  • Abstract

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.

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@Article{NMTMA-9-358, author = {Chao Liang and Xueshuang Xiang}, title = {Convergence of an Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems }, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {3}, pages = {358--382}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2016.m1505}, url = {http://global-sci.org/intro/article_detail/nmtma/12381.html} }
TY - JOUR T1 - Convergence of an Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems AU - Chao Liang & Xueshuang Xiang JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 358 EP - 382 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2016.m1505 UR - https://global-sci.org/intro/article_detail/nmtma/12381.html KW - AB -

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.

Chao Liang and Xueshuang Xiang. (2016). Convergence of an Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems . Numerical Mathematics: Theory, Methods and Applications. 9 (3). 358-382. doi:10.4208/nmtma.2016.m1505
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