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An adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures


Authors: Gang Bao, Peijun Li and Haijun Wu
Journal: Math. Comp. 79 (2010), 1-34
MSC (2000): Primary 65N30, 78A45, 35Q60
DOI: https://doi.org/10.1090/S0025-5718-09-02257-1
Published electronically: May 7, 2009
MathSciNet review: 2552215
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Abstract: An edge element adaptive strategy with error control is developed for wave scattering by biperiodic structures. The unbounded computational domain is truncated to a bounded one by a perfectly matched layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. Numerical experiments are presented to illustrate the competitive behavior of the proposed adaptive method.


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Additional Information

Gang Bao
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: bao@math.msu.edu

Peijun Li
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: lipeijun@math.purdue.edu

Haijun Wu
Affiliation: Department of Mathematics, Nanjing University, Jiangsu, 210093, China
Email: hjw@nju.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-09-02257-1
Keywords: Adaptivity, perfectly matched layer, \textit {a posteriori} error analysis, cross gratings
Received by editor(s): March 19, 2008
Received by editor(s) in revised form: January 1, 2009
Published electronically: May 7, 2009
Additional Notes: The first author’s research was supported in part by the NSF grants DMS-0604790, CCF-0514078, CCF-0830161, and EAR-0724527, the ONR grants N000140210365 and N000140910384, the National Science Foundation of China grant 10428105.
The second author’s research was supported in part by the NSF EAR-0724656.
The third author’s research was supported by the national basic research program under grant 2005CB321701, by the program for new century excellent talents in university of China, and by the NSF of China grant 10401016.
Article copyright: © Copyright 2009 American Mathematical Society
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