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An Adaptive Perfectly Matched Layer Method for Multiple Cavity Scattering Problems

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  01 February 2016

Xinming Wu  and
Weiying Zheng
Xinming Wu*
Affiliation:
The Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China
Weiying Zheng
Affiliation:
NCMIS, LSEC, ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, P.R. China
*
*Corresponding author. Email addresses:[email protected] (X. Wu), [email protected] (W. Zheng)
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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.

Keywords

Uniaxial perfectly matched layermultiple cavity scatteringadaptive finite elementa posteriori error estimate

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N50: Mesh generation and refinement
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 2 , February 2016 , pp. 534 - 558
Copyright
Copyright © Global-Science Press 2016 

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