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Numerical Solution of Acoustic Scattering by an Adaptive DtN Finite Element Method

Published online by Cambridge University Press:  03 June 2015

Xue Jiang ,
Peijun Li  and
Weiying Zheng
Xue Jiang*
Affiliation:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
Peijun Li*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana, 47907, USA
Weiying Zheng*
Affiliation:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, China
*
Email:[email protected]
Corresponding author.Email:[email protected]
Email:[email protected]
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Abstract

Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions, where the wave propagation is governed by the Helmholtz equation. The scattering problem is modeled as a boundary value problem over a bounded domain. Based on the Dirichlet-to-Neumann (DtN) operator, a transparent boundary condition is introduced on an artificial circular boundary enclosing the obstacle. An adaptive finite element based on a posterior error estimate is presented to solve the boundary value problem with a nonlocal DtN boundary condition. Numerical experiments are included to compare with the perfectly matched layer (PML) method to illustrate the competitive behavior of the proposed adaptive method.

Keywords

65M3078A4535Q60Helmholtz equationDtN boundary conditionadaptive finite element methoda posteriori error estimate
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 5 , May 2013 , pp. 1277 - 1244
Copyright
Copyright © Global Science Press Limited 2013

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