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Volume 1, Issue 2
An Adaptive Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems

Zhiming Chen & Xinming Wu

Numer. Math. Theor. Meth. Appl., 1 (2008), pp. 113-137.

Published online: 2008-01

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  • Abstract

The uniaxial perfectly matched layer (PML) method uses rectangular domain to define the PML problem and thus provides greater flexibility and efficiency in dealing with problems involving anisotropic scatterers. In this paper an adaptive uniaxial PML technique for solving the time harmonic Helmholtz scattering problem is developed. The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates. The adaptive finite element method based on a posteriori error estimate is proposed to solve the PML equation which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the PML absorbing layer. Numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method. In particular, it is demonstrated that the PML layer can be chosen as close to one wave-length from the scatterer and still yields good accuracy and efficiency in approximating the far fields.

  • Keywords

Adaptivity, uniaxial perfectly matched layer, a posteriori error analysis, acoustic scattering problems.

  • AMS Subject Headings

65N30, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-1-113, author = {}, title = {An Adaptive Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2008}, volume = {1}, number = {2}, pages = {113--137}, abstract = {

The uniaxial perfectly matched layer (PML) method uses rectangular domain to define the PML problem and thus provides greater flexibility and efficiency in dealing with problems involving anisotropic scatterers. In this paper an adaptive uniaxial PML technique for solving the time harmonic Helmholtz scattering problem is developed. The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates. The adaptive finite element method based on a posteriori error estimate is proposed to solve the PML equation which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the PML absorbing layer. Numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method. In particular, it is demonstrated that the PML layer can be chosen as close to one wave-length from the scatterer and still yields good accuracy and efficiency in approximating the far fields.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6044.html} }
TY - JOUR T1 - An Adaptive Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 113 EP - 137 PY - 2008 DA - 2008/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6044.html KW - Adaptivity, uniaxial perfectly matched layer, a posteriori error analysis, acoustic scattering problems. AB -

The uniaxial perfectly matched layer (PML) method uses rectangular domain to define the PML problem and thus provides greater flexibility and efficiency in dealing with problems involving anisotropic scatterers. In this paper an adaptive uniaxial PML technique for solving the time harmonic Helmholtz scattering problem is developed. The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates. The adaptive finite element method based on a posteriori error estimate is proposed to solve the PML equation which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the PML absorbing layer. Numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method. In particular, it is demonstrated that the PML layer can be chosen as close to one wave-length from the scatterer and still yields good accuracy and efficiency in approximating the far fields.

Zhiming Chen & Xinming Wu. (2020). An Adaptive Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems. Numerical Mathematics: Theory, Methods and Applications. 1 (2). 113-137. doi:
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