Commun. Comput. Phys., 13 (2013), pp. 1227-1244.


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

Xue Jiang 1, Peijun Li 2*, Weiying Zheng 3

1 LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China.
2 Department of Mathematics, Purdue University, West Lafayette, Indiana, 47907, USA.
3 LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, China.

Received 30 October 2011; Accepted (in revised version) 27 April 2012
Available online 8 October 2012
doi:10.4208/cicp.301011.270412a

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.

AMS subject classifications: 65M30, 78A45, 35Q60

Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Helmholtz equation, DtN boundary condition, adaptive finite element method, a posteriori error estimate.

*Corresponding author.
Email: jxue@lsec.cc.ac.cn (X. Jiang), lipeijun@math.purdue.edu (P. Li), zwy@lsec.cc.ac.cn (W. Zheng)
 

The Global Science Journal