Commun. Comput. Phys., 5 (2009), pp. 546-564.

An hp Adaptive Uniaxial Perfectly Matched Layer Method for Helmholtz Scattering Problems

Zhiming Chen 1*, Benqi Guo 2, Yuanming Xiao 1

1 Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China.
2 Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada.

Received 17 September 2007; Accepted (in revised version) 9 December 2007
Available online 1 August 2008


We propose an adaptive strategy for solving high frequency Helmholtz scattering problems. The method is based on the uniaxial PML method to truncate the scattering problem which is defined in the unbounded domain into the bounded domain. The parameters in the uniaxial PML method are determined by sharp a posteriori error estimates developed by Chen and Wu \cite{cw}. An $hp$-adaptive finite element strategy is proposed to solve the uniaxial PML equation. Numerical experiments are included which indicate the desirable exponential decay property of the error.

AMS subject classifications: 65N30, 65N35, 65N50, 35J05

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Key words: Adaptivity, uniaxial perfectly matched layer, time-harmonic scattering, Helmholtz equation, hp-finite element method.

*Corresponding author.
Email: (Z. Chen), (B. Q. Guo), (Y. M. Xiao)

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