Numerical integration over the square in the presence of algebraic/logarithmic singularities with an application to aerodynamics

被引：8

作者：

Gautschi, Walter ^{[1
]}

机构：

[1] Purdue Univ, Dept Comp Sci, W Lafayette, IN 47907 USA

来源：

NUMERICAL ALGORITHMS | 2012年 / 61卷 / 02期

关键词：

Numerical integration over the square; Algebraic/logarithmic singular lines along the diagonal and the sides of the square; Gaussian quadrature; Aerodynamical drag coefficient;

D O I：

10.1007/s11075-012-9611-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Tensor-product formulae based on one-dimensional Gaussian quadratures are developed for evaluating double integrals of the type indicated in the title. If the singularities occur only along the diagonal and the regular part of the integrand is a polynomial of total degree d, the formulae can be made exact by choosing the number of quadrature points larger than, or equal to, 1 + d/2. Numerical examples are given as well as an application to a problem in aerodynamics.

引用

页码：275 / 290

页数：16

共 17 条

[1] Numerical integration over the square in the presence of algebraic/logarithmic singularities with an application to aerodynamics
Walter Gautschi
Numerical Algorithms, 2012, 61 : 275 - 290
[2] Erratum to: Numerical integration over the square in the presence of algebraic/logarithmic singularities with an application to aerodynamics
Walter Gautschi
Numerical Algorithms, 2013, 64 : 759 - 759
[3] Numerical integration over the square in the presence of algebraic/logarithmic singularities with an application to aerodynamics (vol 61, pg 275, 2012)
Gautschi, Walter
NUMERICAL ALGORITHMS, 2013, 64 (04) : 759 - 759
[4] NUMERICAL INTEGRATION IN THE PRESENCE OF SINGULARITIES
P.A.P.Moran
数学物理学报, 1981, (01) : 83 - 85
[5] NUMERICAL INTEGRATION IN THE PRESENCE OF SINGULARITIES
P.A.P.Moran
Acta Mathematica Scientia, 1981, (01) : 83 - 85
[6] Efficient Cubature Rules for the Numerical Integration of Logarithmic Singularities
Niegemann, J.
2014 INTERNATIONAL CONFERENCE ON ELECTROMAGNETICS IN ADVANCED APPLICATIONS (ICEAA), 2014, : 601 - 604
[7] SIMPLE NUMERICAL-INTEGRATION OF LOGARITHMIC SINGULARITIES IN MOMENT METHOD SOLUTIONS OF ELECTROMAGNETIC PROBLEMS
AUBREY, T
WHITE, P
ELECTRONICS LETTERS, 1992, 28 (16) : 1519 - 1521
[8] On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities
Trindade, M.A.
Sampaio, R.
Revista Brasileira de Ciencias Mecanicas/Journal of the Brazilian Society of Mechanical Sciences, 2001, 23 (01): : 49 - 62
[9] EULER-MACLAURIN EXPANSIONS FOR INTEGRALS OVER TRIANGLES AND SQUARES OF FUNCTIONS HAVING ALGEBRAIC LOGARITHMIC SINGULARITIES ALONG AN EDGE
SIDI, A
JOURNAL OF APPROXIMATION THEORY, 1983, 39 (01) : 39 - 53
[10] NUMERICAL QUADRATURE AND NON-LINEAR SEQUENCE TRANSFORMATIONS - UNIFIED RULES FOR EFFICIENT COMPUTATION OF INTEGRALS WITH ALGEBRAIC AND LOGARITHMIC ENDPOINT SINGULARITIES
SIDI, A
MATHEMATICS OF COMPUTATION, 1980, 35 (151) : 851 - 874

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