BOUNDARY ELEMENT COLLOCATION METHOD FOR SOLVING THE EXTERIOR NEUMANN PROBLEM FOR HELMHOLTZ'S EQUATION IN THREE DIMENSIONS

被引：0

作者：

Kleefeld, Andreas ^{[1
]}

Lin, Tzu-Chu ^{[2
]}

机构：

[1] Brandenburg Tech Univ Cottbus, D-03046 Cottbus, Germany

[2] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2012年 / 39卷

关键词：

Fredholm integral equation of the second kind; Helmholtz's equation; exterior Neumann problem; boundary element collocation method; superconvergence; INTEGRAL-EQUATIONS; NUMERICAL-SOLUTION; CONDITION NUMBER; T-MATRIX; SCATTERING; RADIATION; FORMULATION; ACOUSTICS; OPERATORS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe a boundary integral equation that solves the exterior Neumann problem for the Helmholtz equation in three dimensions. The unique solution is found by approximating a Fredholm integral equation of the second kind with the boundary element collocation method. We prove superconvergence at the collocation points, distinguishing the cases of even and odd interpolation. Numerical examples demonstrate the performance of the method solving the integral equation and confirm the superconvergence.

引用

页码：113 / 143

页数：31

共 45 条

[1] AN INVESTIGATION OF BOUNDARY ELEMENT METHODS FOR THE EXTERIOR ACOUSTIC PROBLEM [J].

AMINI, S ;

WILTON, DT .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1986, 54 (01) :49-65

[2] Alternative integral equations for the iterative solution of acoustic scattering problems [J].

Antoine, X ;

Darbas, M .

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 2005, 58 :107-128

[3] PIECEWISE CONTINUOUS COLLOCATION FOR INTEGRAL-EQUATIONS [J].

ATKINSON, K ;

GRAHAM, I ;

SLOAN, I .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (01) :172-186

[4]

Atkinson K., 1997, NUMERICAL SOLUTION I, DOI DOI 10.1017/CBO9780511626340

[5]

ATKINSON K.E., 1998, J INTEGRAL EQUATIONS, V10, P253, DOI DOI 10.1216/JIEA/1181074231

[6] PIECEWISE POLYNOMIAL COLLOCATION FOR BOUNDARY INTEGRAL-EQUATIONS [J].

ATKINSON, KE ;

CHIEN, D .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1995, 16 (03) :651-681

[7] Condition Number Estimates for Combined Potential Integral Operators in Acoustics and Their Boundary Element Discretisation [J].

Betcke, T. ;

Chandler-Wilde, S. N. ;

Graham, I. G. ;

Langdon, S. ;

Lindner, M. .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2011, 27 (01) :31-69

[8] On the acoustic single layer potential: Stabilization and Fourier analysis [J].

Buffa, A. ;

Sauter, S. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2006, 28 (05) :1974-1999

[9] Regularized combined field integral equations [J].

Buffa, A ;

Hiptmair, R .

NUMERISCHE MATHEMATIK, 2005, 100 (01) :1-19

[10]

BURTON A. J., 1976, NUMERICAL SOLUTION A

← 1 2 3 4 5 →