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

被引：19

作者：

Jiang, Xue ^{[1
]}

Li, Peijun ^{[2
]}

Zheng, Weiying ^{[3
]}

机构：

[1] Chinese Acad Sci, LSEC, Inst Computat Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[3] Chinese Acad Sci, LSEC, Inst Computat Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2013年 / 13卷 / 05期

关键词：

Helmholtz equation; DtN boundary condition; adaptive finite element method; a posteriori error estimate; HIGH WAVE-NUMBER; BOUNDARY-CONDITIONS; HELMHOLTZ-EQUATION; FEM; OPERATORS; VERSION;

D O I：

10.4208/cicp.301011.270412a

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：1227 / 1244

页数：18

共 21 条

[1]

Adams A., 2003, Sobolev Spaces, V140

[2]

[Anonymous], 1983, ELLIPTIC PARTIAL DIF

[3]

[Anonymous], PREPRINT

[4]

BABUSKA I, 1973, SURVEY LECT MATH FDN, P5

[5] An adaptive perfectly matched layer technique for time-harmonic scattering problems [J].

Chen, ZM ;

Liu, XZ .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2005, 43 (02) :645-671

[6] An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures [J].

Chen, ZM ;

Wu, HJ .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2003, 41 (03) :799-826

[7]

Colton D., 1998, INVERSE ACOUSTIC ELE

[8]

Colton D., 1983, INTEGRAL EQUATION ME

[9]

ENGQUIST B, 1977, MATH COMPUT, V31, P629, DOI 10.1090/S0025-5718-1977-0436612-4

[10] Dirichlet-to-Neumann boundary conditions for multiple scattering problems [J].

Grote, MJ ;

Kirsch, C .

JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 201 (02) :630-650

← 1 2 3 →