Strongly and uniformly convergent Green's function expansions

Fikioris, JG; Tsalamengas, JL

dc.contributor.author	Fikioris, JG	en
dc.contributor.author	Tsalamengas, JL	en
dc.date.accessioned	2014-03-01T01:06:59Z
dc.date.available	2014-03-01T01:06:59Z
dc.date.issued	1987	en
dc.identifier.issn	0016-0032	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9723
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0023171326&partnerID=40&md5=576a847b938561ed87fcae3fffdd357b	en
dc.subject.classification	Automation & Control Systems	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	DIELECTRIC MATERIALS - Calculations	en
dc.subject.other	MATHEMATICAL TRANSFORMATIONS	en
dc.subject.other	CONVERGENCE	en
dc.subject.other	SOURCE POINT	en
dc.subject.other	WATSON TRANSFORMATION	en
dc.subject.other	MATHEMATICAL TECHNIQUES	en
dc.title	Strongly and uniformly convergent Green's function expansions	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1987	en
heal.abstract	The convergence of Green's function expansions used in the exact analytical treatment of problems involving boundaries of different shapes is a property crucial in obtaining their solution. Existing expansions in most cases suffer from two serious setbacks: they do not converge uniformly in their region of validity, exhibiting a slow and conditional convergence near the source (singular) point and, even worse, they change expression when the field point moves past the source point. For such reasons they are unsuited for the solution of singular integral equations, in which values of the Green's function G at the source point do appear inside the integral. These inadequacies are met head-on by extracting the singular behavior in a closed-form term. Additional simple terms are also extracted to improve the convergence of the expansion of the remaining, non-singular part of G. The so-obtained new eigenfunction expansions for G converge uniformly over the whole region of their validity and very strongly (exponentially) near the source point. They are particularly suited for the solution of singular integral equations by the Carleman-Vekua method, otherwise known as the method of regularization by solving the dominant equation. These new expansions can be further subjected to a Watson transformation yielding a third expansion exhibiting strong convergence in regions where the convergence of the preceding series weakens, and vise versa. All these considerations are illustrated in this paper by means of a two-dimensional harmonic Green's function of a line source inside a rectangular shield, which is useful in a variety of shieldedline configurations. Extensions to different dielectric sublayers, to wave (Helmholtz) Green's functions, etc., are also discussed. © 1987.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Journal of the Franklin Institute	en
dc.identifier.isi	ISI:A1987J636400001	en
dc.identifier.volume	324	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	17	en