Volume 19, Issue 2
An Adaptive Perfectly Matched Layer Method for Multiple Cavity Scattering Problems

Xinming Wu & Weiying Zheng

Commun. Comput. Phys., 19 (2016), pp. 534-558.

Published online: 2018-04

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  • Abstract

A uniaxial perfectly matched layer (PML) method is proposed for solving the scattering problem with multiple cavities. By virtue of the integral representation of the scattering field, we decompose the problem into a system of single-cavity scattering problems which are coupled with Dirichlet-to-Neumann maps. A PML is introduced to truncate the exterior domain of each cavity such that the computational domain does not intersect those for other cavities. Based on the a posteriori error estimates, an adaptive finite element algorithm is proposed to solve the coupled system. The novelty of the proposed method is that its computational complexity is comparable to that for solving uncoupled single-cavity problems. Numerical experiments are presented to demonstrate the efficiency of the adaptive PML method.

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@Article{CiCP-19-534, author = {Xinming Wu and Weiying Zheng}, title = {An Adaptive Perfectly Matched Layer Method for Multiple Cavity Scattering Problems}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {2}, pages = {534--558}, abstract = {

A uniaxial perfectly matched layer (PML) method is proposed for solving the scattering problem with multiple cavities. By virtue of the integral representation of the scattering field, we decompose the problem into a system of single-cavity scattering problems which are coupled with Dirichlet-to-Neumann maps. A PML is introduced to truncate the exterior domain of each cavity such that the computational domain does not intersect those for other cavities. Based on the a posteriori error estimates, an adaptive finite element algorithm is proposed to solve the coupled system. The novelty of the proposed method is that its computational complexity is comparable to that for solving uncoupled single-cavity problems. Numerical experiments are presented to demonstrate the efficiency of the adaptive PML method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.040215.280815a}, url = {http://global-sci.org/intro/article_detail/cicp/11099.html} }
TY - JOUR T1 - An Adaptive Perfectly Matched Layer Method for Multiple Cavity Scattering Problems AU - Xinming Wu & Weiying Zheng JO - Communications in Computational Physics VL - 2 SP - 534 EP - 558 PY - 2018 DA - 2018/04 SN - 19 DO - http://dor.org/10.4208/cicp.040215.280815a UR - https://global-sci.org/intro/cicp/11099.html KW - AB -

A uniaxial perfectly matched layer (PML) method is proposed for solving the scattering problem with multiple cavities. By virtue of the integral representation of the scattering field, we decompose the problem into a system of single-cavity scattering problems which are coupled with Dirichlet-to-Neumann maps. A PML is introduced to truncate the exterior domain of each cavity such that the computational domain does not intersect those for other cavities. Based on the a posteriori error estimates, an adaptive finite element algorithm is proposed to solve the coupled system. The novelty of the proposed method is that its computational complexity is comparable to that for solving uncoupled single-cavity problems. Numerical experiments are presented to demonstrate the efficiency of the adaptive PML method.

Xinming Wu & Weiying Zheng. (1970). An Adaptive Perfectly Matched Layer Method for Multiple Cavity Scattering Problems. Communications in Computational Physics. 19 (2). 534-558. doi:10.4208/cicp.040215.280815a
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