• myGriffith
    • Staff portal
    • Contact Us⌄
      • Future student enquiries 1800 677 728
      • Current student enquiries 1800 154 055
      • International enquiries +61 7 3735 6425
      • General enquiries 07 3735 7111
      • Online enquiries
      • Staff phonebook
    View Item 
    •   Home
    • Griffith Research Online
    • Journal articles
    • View Item
    • Home
    • Griffith Research Online
    • Journal articles
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

  • All of Griffith Research Online
    • Communities & Collections
    • Authors
    • By Issue Date
    • Titles
  • This Collection
    • Authors
    • By Issue Date
    • Titles
  • Statistics

  • Most Popular Items
  • Statistics by Country
  • Most Popular Authors
  • Support

  • Contact us
  • FAQs
  • Admin login

  • Login
  • The iterated sinh transformation

    Thumbnail
    View/Open
    53196_1.pdf (99.34Kb)
    Author(s)
    Elliott, David
    Johnston, Peter R
    Griffith University Author(s)
    Johnston, Peter R.
    Year published
    2008
    Metadata
    Show full item record
    Abstract
    A sinh transformation has recently been proposed to improve the numerical accuracy of evaluating nearly singular integrals using Gauss-Legendre quadrature. It was shown that the transformation could improve the accuracy of evaluating such integrals, which arise in the boundary element method, by several orders of magnitude. Here, this transformation is extended in an iterative fashion to allow the accurate evaluation of similar types of integrals that have more spiked integrands. Results show that one iteration of this sinh transformation is preferred for nearly weakly singular integrals, whereas two iterations lead to ...
    View more >
    A sinh transformation has recently been proposed to improve the numerical accuracy of evaluating nearly singular integrals using Gauss-Legendre quadrature. It was shown that the transformation could improve the accuracy of evaluating such integrals, which arise in the boundary element method, by several orders of magnitude. Here, this transformation is extended in an iterative fashion to allow the accurate evaluation of similar types of integrals that have more spiked integrands. Results show that one iteration of this sinh transformation is preferred for nearly weakly singular integrals, whereas two iterations lead to several orders of magnitude improvement in the evaluation of nearly strongly singular integrals. The same observation applies when considering integrals of derivatives of the two-dimensional boundary element kernel. However, for these integrals, more iterations are required as the distance from the source point to the boundary element decreases.
    View less >
    Journal Title
    International Journal for Numerical Methods in Engineering
    Volume
    75
    Issue
    1
    DOI
    https://doi.org/10.1002/nme.2244
    Copyright Statement
    © 2008 John Wiley & Sons, Ltd. This is the pre-peer reviewed version of the following article: The iterated sinh transformation International Journal for Numerical Methods in Engineering, Vol. 75(1), 2008, pp. 43-57, which has been published in final form at http://dx.doi.org/10.1002/nme.2244
    Subject
    Numerical analysis
    Engineering
    Publication URI
    http://hdl.handle.net/10072/22494
    Collection
    • Journal articles

    Footer

    Disclaimer

    • Privacy policy
    • Copyright matters
    • CRICOS Provider - 00233E
    • TEQSA: PRV12076

    Tagline

    • Gold Coast
    • Logan
    • Brisbane - Queensland, Australia
    First Peoples of Australia
    • Aboriginal
    • Torres Strait Islander