Inmost singularities of S.I.Es influencing their numerical solution in the BEM

Tsamasphyros, G; Theotokoglou, EE

dc.contributor.author	Tsamasphyros, G	en
dc.contributor.author	Theotokoglou, EE	en
dc.date.accessioned	2014-03-01T01:28:41Z
dc.date.available	2014-03-01T01:28:41Z
dc.date.issued	2008	en
dc.identifier.issn	0955-7997	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18916
dc.subject	Boundary element method	en
dc.subject	Elasticity	en
dc.subject	Inmost singularities	en
dc.subject	Nearby poles	en
dc.subject	Numerical integration	en
dc.subject	Quadrature formula	en
dc.subject	Singular integral equation	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	Boundary element method	en
dc.subject.other	Numerical methods	en
dc.subject.other	Problem solving	en
dc.subject.other	Cauchy singularity	en
dc.subject.other	Inmost singularities	en
dc.subject.other	Nearby poles	en
dc.subject.other	Point singularities	en
dc.subject.other	Quadrature formula	en
dc.subject.other	Unknown function	en
dc.subject.other	Integral equations	en
dc.title	Inmost singularities of S.I.Es influencing their numerical solution in the BEM	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.enganabound.2007.08.008	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.enganabound.2007.08.008	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	When solving numerically the singular integral equations (S.I.Es) using the boundary element method (BEM) or other similar methods, special attention is given to the Cauchy singularity of the singular integrals and to the end point singularities of the unknown function. But in many cases there exist other, inmost, singularities either in the unknown function or in the regular kernel. In fact the unknown function can have essential singularities (poles of order one or two), weak singularities and nearby singularities at isolated points. Usually these singularities are provoked from singularities of the right hand side (r.h.s.) function, whereas the regular kernel can have essential and weak singularities at isolated points and nearby singularities. Neglecting these singularities in the numerical process, we obtain solutions largely diverging from the exact ones. So far these problems are not confronted in the BEM numerical process. In this paper, we classify all these singularities and we give two numerical examples illustrating the important influence of nearby singularities of the regular kernel. Some suggestions concerning appropriate numerical methods for these problems are also given. (c) 2007 Elsevier Ltd. All rights reserved.	en
heal.publisher	ELSEVIER SCI LTD	en
heal.journalName	Engineering Analysis with Boundary Elements	en
dc.identifier.doi	10.1016/j.enganabound.2007.08.008	en
dc.identifier.isi	ISI:000253752800001	en
dc.identifier.volume	32	en
dc.identifier.issue	3	en
dc.identifier.spage	187	en
dc.identifier.epage	195	en