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dc.contributor.authorJohnston, Barbara M
dc.contributor.authorJohnston, Peter R
dc.contributor.authorElliot, David
dc.date.accessioned2017-05-03T13:56:21Z
dc.date.available2017-05-03T13:56:21Z
dc.date.issued2007
dc.date.modified2009-09-21T05:48:31Z
dc.identifier.issn0029-5981
dc.identifier.doi10.1002/nme.1816
dc.identifier.urihttp://hdl.handle.net/10072/15063
dc.description.abstractAn implementation of the boundary element method requires the accurate evaluation of many integrals. When the source point is far from the boundary element under consideration, a straightforward application of Gaussian quadrature suffices to evaluate such integrals. When the source point is on the element, the integrand becomes singular and accurate evaluation can be obtained using the same Gaussian points transformed under a polynomial transformation which has zero Jacobian at the singular point. A class of integrals which lies between these two extremes is that of nearly singular integrals. Here, the source point is close to, but not on, the element and the integrand remains finite at all points. However, instead of remaining flat, the integrand develops a sharp peak as the source point moves closer to the element, thus rendering accurate evaluation of the integral difficult. This paper presents a transformation, based on the sinh function, which automatically takes into account the position of the projection of the source point onto the element, which we call the nearly singular point, and the distance from the source point to the element. The transformation again clusters the points towards the nearly singular point, but does not have a zero Jacobian. Implementation of the transformation is straightforward and could easily be included in existing boundary element method software. It is shown that, for the two-dimensional boundary element method, several orders of magnitude improvement in relative error can be obtained using this transformation compared to a conventional implementation of Gaussian quadrature. Asymptotic estimates for the truncation errors are also quoted.
dc.description.peerreviewedYes
dc.description.publicationstatusYes
dc.languageEnglish
dc.language.isoeng
dc.publisherJohn Wiley & Sons Ltd.
dc.publisher.placeUnited Kingdom
dc.publisher.urihttps://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1816
dc.relation.ispartofstudentpublicationN
dc.relation.ispartofpagefrom1460
dc.relation.ispartofpageto1479
dc.relation.ispartofissue7
dc.relation.ispartofjournalInternational Journal for Numerical Methods in Engineering
dc.relation.ispartofvolume69
dc.rights.retentionY
dc.subject.fieldofresearchEngineering
dc.subject.fieldofresearchcode40
dc.titleA sinh transformation for evaluating two-dimensional nearly singular boundary element integrals
dc.typeJournal article
dc.type.descriptionC1 - Articles
dc.type.codeC - Journal Articles
gro.facultyGriffith Sciences, School of Natural Sciences
gro.rights.copyright© 2007 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.
gro.date.issued2007
gro.hasfulltextNo Full Text
gro.griffith.authorJohnston, Barbara M.
gro.griffith.authorJohnston, Peter R.


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