Quadrature rules for weakly singular, strongly singular, and hypersingular integrals in boundary integral equation methods

被引：22

作者：

Tsalamengas, John L. ^{[1
]}

机构：

[1] Natl Tech Univ Athens, Sch Elect & Comp Engn, GR-15773 Athens, Greece

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2015年 / 303卷

关键词：

Quadrature rules; Singular integrals; Hypersingular integrals; Integral equations; Nystrom method; PRINCIPAL VALUE INTEGRALS; HADAMARD-TYPE SINGULARITIES; NUMERICAL-SOLUTION; 2ND KIND; CAUCHY; CONVERGENCE; FORMULAS; SYSTEMS; 2-D;

D O I：

10.1016/j.jcp.2015.09.053

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We present n-point Gauss-Gegenbauer quadrature rules for weakly singular, strongly singular, and hypersingular integrals that arise in integral equation formulations of potential problems in domains with edges and corners. The rules are tailored to weight functions with algebraic endpoint singularities related to the geometrical singularities of the domain. Each rule has two different expressions involving Legendre functions and hypergeometric functions, respectively. Numerical examples amply demonstrate the accuracy and stability of the proposed algorithms. Application to the solution of a singular integral equation is exemplified. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：498 / 513

页数：16

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