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A new method for the numerical evaluation of nearly singular integrals on triangular elements in the 3D boundary element method

Citation

Johnston, BM and Johnston, PR and Elliott, D, A new method for the numerical evaluation of nearly singular integrals on triangular elements in the 3D boundary element method, Journal of Computational and Applied Mathematics, 245 pp. 148-161. ISSN 0377-0427 (2013) [Refereed Article]

Copyright Statement

Copyright 2013 Elsevier B.V.

DOI: doi:10.1016/j.cam.2012.12.018

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.

Item Details

Item Type:Refereed Article
Keywords:Numerical integration, nearly singular integrals, boundary element method, sinh transformation
Research Division:Mathematical Sciences
Research Group:Numerical and Computational Mathematics
Research Field:Numerical Solution of Differential and Integral Equations
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Elliott, D (Professor David Elliott)
ID Code:85135
Year Published:2013
Web of Science® Times Cited:22
Deposited By:Mathematics and Physics
Deposited On:2013-06-14
Last Modified:2015-01-27
Downloads:0

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