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  • A Simple Device to Improve the Accuracy of Evaluating Weakly Singular Boundary Element Integrals

    Author(s)
    Johnston, PR
    Johnston, BA
    Griffith University Author(s)
    Johnston, Barbara M.
    Johnston, Peter R.
    Year published
    2002
    Metadata
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    Abstract
    The question of the accurate numerical evaluation of weakly singular integrals arising in the boundary element method has attracted considerable recent attention. A popular method is to use a non-linear transformation with zero derivative at the singular point to adjust the position of the Gauss-Legendre quadrature points, resulting in a more accurate evaluation of the integral. This paper presents a simple algebraic device to overcome a numerical round-off problem which has limited previous implementations of non-linear transformations. Utilization of this device allows higher orders of transformation to be used, resulting ...
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    The question of the accurate numerical evaluation of weakly singular integrals arising in the boundary element method has attracted considerable recent attention. A popular method is to use a non-linear transformation with zero derivative at the singular point to adjust the position of the Gauss-Legendre quadrature points, resulting in a more accurate evaluation of the integral. This paper presents a simple algebraic device to overcome a numerical round-off problem which has limited previous implementations of non-linear transformations. Utilization of this device allows higher orders of transformation to be used, resulting in lower relative errors in the numerical evaluation of the weakly singular integrals.
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    Journal Title
    Communications in Numerical Methods in Engineering
    Volume
    18
    Publisher URI
    https://onlinelibrary.wiley.com/doi/10.1002/cnm.482
    DOI
    https://doi.org/10.1002/cnm.482
    Copyright Statement
    © 2002 John Wiley & Sons, Ltd. Self-archiving of the author-manuscript version is not yet supported by this publisher. Please refer to the journal link for access to the definitive, published version or contact the author for more information.
    Subject
    Mathematical sciences
    Engineering
    Publication URI
    http://hdl.handle.net/10072/6995
    Collection
    • Journal articles

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