The analytic form of Green's function in elliptic coordinates

Chatjigeorgiou, IK; Mavrakos, SA

dc.contributor.author	Chatjigeorgiou, IK	en
dc.contributor.author	Mavrakos, SA	en
dc.date.accessioned	2014-03-01T02:14:47Z
dc.date.available	2014-03-01T02:14:47Z
dc.date.issued	2012	en
dc.identifier.issn	00220833	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/30119
dc.subject	Addition theorems	en
dc.subject	Boundary value problem	en
dc.subject	Elliptical cylinders	en
dc.subject	Inhomogeneous Helmholtz equation	en
dc.subject.other	Addition theorem	en
dc.subject.other	Analytic solution	en
dc.subject.other	Boundary values	en
dc.subject.other	Closed form solutions	en
dc.subject.other	Closed-form formulae	en
dc.subject.other	Diffraction problem	en
dc.subject.other	Elliptic coordinates	en
dc.subject.other	Elliptical cylinder	en
dc.subject.other	Green's theorem	en
dc.subject.other	Incident waves	en
dc.subject.other	Inhomogeneous Helmholtz equations	en
dc.subject.other	Mathematical analysis	en
dc.subject.other	Polar coordinate	en
dc.subject.other	Second orders	en
dc.subject.other	Velocity potentials	en
dc.subject.other	Wave components	en
dc.subject.other	Cylinders (shapes)	en
dc.subject.other	Diffraction	en
dc.subject.other	Helmholtz equation	en
dc.subject.other	Green's function	en
dc.title	The analytic form of Green's function in elliptic coordinates	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10665-011-9464-6	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10665-011-9464-6	en
heal.publicationDate	2012	en
heal.abstract	The purpose of this study is the derivation of a closed-form formula for Green's function in elliptic coordinates that could be used for achieving an analytic solution for the second-order diffraction problem by elliptical cylinders subjected to monochromatic incident waves. In fact, Green's function represents the solution of the so-called locked wave component of the second-order velocity potential. The mathematical analysis starts with a proper analytic formulation of the second-order diffraction potential that results in the inhomogeneous Helmholtz equation. The associated boundary-value problem is treated by applying Green's theorem to obtain a closed-form solution for Green's function. Green's function is initially expressed in polar coordinates while its final elliptic form is produced through the proper employment of addition theorems. © 2011 Springer Science+Business Media B.V.	en
heal.journalName	Journal of Engineering Mathematics	en
dc.identifier.doi	10.1007/s10665-011-9464-6	en
dc.identifier.volume	72	en
dc.identifier.issue	1	en
dc.identifier.spage	87	en
dc.identifier.epage	105	en