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

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    Author(s)
    Johnston, Barbara M
    Johnston, Peter R
    Elliott, David
    Griffith University Author(s)
    Johnston, Barbara M.
    Johnston, Peter R.
    Year published
    2013
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    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 ...
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    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.
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    Journal Title
    Journal of Computational and Applied Mathematics
    Volume
    245
    DOI
    https://doi.org/10.1016/j.cam.2012.12.018
    Copyright Statement
    © 2013 Elsevier B.V. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
    Subject
    Applied mathematics
    Approximation theory and asymptotic methods
    Numerical and computational mathematics
    Publication URI
    http://hdl.handle.net/10072/54329
    Collection
    • Journal articles

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