Paper Info
Title
A New Sigmoidal Transformation for Weakly Singular Integrals in the Boundary Element Method
Abstract
The power of the sigmoidal transformation in weakly singular integrals has been demonstrated by the recent works [A. Sidi, in Numerical Integration IV, H. Brass and G. Hämmerlin, eds., Birkhäuser--Verlag, Berlin, 1993, pp. 359--373; P. R. Johnston, Internat. J. Numer. Methods Engrg., 45 (1999), pp. 1333--1348; P. R. Johnston, Internat. J. Numer. Methods Engrg., 47 (2000), pp. 1709--1730; D. Elliott, Math. Methods Appl. Sci., 20 (1997), pp. 121--132; D. Elliott, J. Austral. Math. Soc. Ser. B, 40 (1998), pp. E77--E137]. Especially, application of this transformation is useful for efficient numerical evaluation of the singular integrals appearing in the usual boundary element method. In this paper, a new sigmoidal transformation containing a parameter b is presented. It is shown that the present transformation, with the Gauss--Legendre quadrature rule, can improve the asymptotic truncation error of the traditional sigmoidal transformations by controlling the parameter. For some examples, we compare the numerical results of the present method with those of the well-known Sidi- and Elliott-transformations to show the superiority of the former.
Year
DOI
Venue
2003
10.1137/S1064827501396191
SIAM Journal on Scientific Computing
Keywords
DocType
Volume
weakly singular integrals,traditional sigmoidal transformation,sigmoidal transformation,new sigmoidal transformation,methods appl,j. numer,p. r,present transformation,boundary element method,j. austral,efficient numerical evaluation,methods engrg,singular integral
Journal
24
Issue
ISSN
Citations 
4
1064-8275
3
PageRank 
References 
Authors
1.10
0
2
Name
Order
Citations
PageRank
Beong In Yun18612.55
Philsu Kim2298.78