Numerical Solution of Acoustic Scattering by an Adaptive DtN Finite Element Method
Xue Jiang 1, Peijun Li 2*, Weiying Zheng 31 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
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
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Key words: Helmholtz equation, DtN boundary condition, adaptive finite element method, a posteriori error estimate.
Email: firstname.lastname@example.org (X. Jiang), email@example.com (P. Li), firstname.lastname@example.org (W. Zheng)