University Of Tasmania

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

journal contribution
posted on 2023-05-17, 18:25 authored by Johnston, BM, Johnston, PR, David ElliottDavid Elliott
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.


Publication title

Journal of Computational and Applied Mathematics








School of Natural Sciences


Elsevier Science Bv

Place of publication

Po Box 211, Amsterdam, Netherlands, 1000 Ae

Rights statement

Copyright 2013 Elsevier B.V.

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences