Closed-Form Evaluation of Potential Integrals in the Boundary Element Method

被引：1

作者：

Carley, Michael ^{[1
]}

机构：

[1] Univ Bath, Dept Mech Engn, Bath BA2 7AY, Avon, England

来源：

JOURNAL OF THEORETICAL AND COMPUTATIONAL ACOUSTICS | 2020年 / 28卷 / 02期

关键词：

Boundary element method; numerical integration; layer potentials; Helmholtz equation; scattering; BEM; REPRESENTATIONS; TRANSFORMATION;

D O I：

10.1142/S2591728519500142

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

A method is presented for the closed-form evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on a plane element, and used to develop a criterion for the selection of quadrature rules. The analytical approach is based on an optimized expansion of the Green's function for the problem, selected to limit the error to some required tolerance. Results are presented showing accuracy to tolerances comparable to machine precision.

引用

页数：20

共 23 条

[1]

Acton F.S., 1990, Numerical Methods that Work, MAA spectrum

[2] APPLICATION OF INTEGRAL EQUATION METHODS TO NUMERICAL SOLUTION OF SOME EXTERIOR BOUNDARY-VALUE PROBLEMS [J].

BURTON, AJ ;

MILLER, GF .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1971, 323 (1553) :201-&

[3] Analytical integrations in 3D BEM: preliminaries [J].

Carini, A ;

Salvadori, A .

COMPUTATIONAL MECHANICS, 2002, 28 (3-4) :177-185

[4] Analytical Formulae for Potential Integrals on Triangles [J].

Carley, Michael J. .

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2013, 80 (04)

[5]

Gradshteyn I. S., 2014, TABLE INTEGRALS SERI

[6] A GENERAL ALGORITHM FOR MULTIDIMENSIONAL CAUCHY PRINCIPAL VALUE INTEGRALS IN THE BOUNDARY ELEMENT METHOD [J].

GUIGGIANI, M ;

GIGANTE, A .

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1990, 57 (04) :906-915

[7]

Gumerov N.A., 2004, FAST MULTIPOLE METHO

[8] Variable transformations for nearly singular integrals in the boundary element method [J].

Hayami, K .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2005, 41 (04) :821-842

[9] SOME NOTES ON SINGULAR INTEGRAL TECHNIQUES IN BOUNDARY-ELEMENT ANALYSIS [J].

HUANG, Q ;

CRUSE, TA .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1993, 36 (15) :2643-2659

[10]

Kirkup S.M., 2007, The Boundary Element Method in Acoustics

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