Paper Info
Title
A new method for the numerical evaluation of nearly singular integrals on triangular elements in the 3D boundary element method.
Abstract
A new method (the sinh-sigmoidal method) is proposed for the numerical evaluation of both nearly weakly and nearly strongly singular integrals on triangular boundary elements. These integrals arise in the 3D boundary element method when the source point is very close to the element of integration. The new polar coordinate-based method introduces a sinh transformation in the radial direction and a sigmoidal transformation in the angular direction, before the application of Gaussian quadrature. It also uses approximately twice as many quadrature points in the angular direction as in the radial direction, in response to a finding that the evaluation of these types of integrals is particularly sensitive to the placement of the quadrature points in the angular direction. Comparisons with various other methods demonstrate its accuracy and competitiveness. A major advantage of the new method is its ease of implementation and applicability to a wide class of integrals.
Year
DOI
Venue
2013
10.1016/j.cam.2012.12.018
J. Computational Applied Mathematics
Keywords
Field
DocType
quadrature point,sigmoidal transformation,singular integral,triangular element,boundary element method,radial direction,angular direction,numerical evaluation,gaussian quadrature,new polar coordinate-based method,sinh-sigmoidal method,new method,numerical integration
Boundary knot method,Mathematical optimization,Singular integral,Mathematical analysis,Numerical integration,Order of integration (calculus),Singular boundary method,Boundary element method,Quadrature (mathematics),Gaussian quadrature,Mathematics
Journal
Volume
ISSN
Citations 
245
0377-0427
6
PageRank 
References 
Authors
1.03
2
3
Name
Order
Citations
PageRank
Barbara M. Johnston1258.44
Peter R. Johnston28015.20
David Elliott361.03