On the oscillations appearing in numerical solutions of solvable and nonsolvable integral equations for thin-wire antennas

Papakanellos, PJ; Fikioris, G; Michalopoulou, A

dc.contributor.author	Papakanellos, PJ	en
dc.contributor.author	Fikioris, G	en
dc.contributor.author	Michalopoulou, A	en
dc.date.accessioned	2014-03-01T01:34:02Z
dc.date.available	2014-03-01T01:34:02Z
dc.date.issued	2010	en
dc.identifier.issn	0018-926X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20653
dc.subject	Antenna feeds	en
dc.subject	Antenna theory	en
dc.subject	Galerkin method	en
dc.subject	Integral equations	en
dc.subject	Wire antennas	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.classification	Telecommunications	en
dc.subject.other	Antenna feeds	en
dc.subject.other	Antenna theory	en
dc.subject.other	Basis functions	en
dc.subject.other	Exact solution	en
dc.subject.other	Ill posed	en
dc.subject.other	Method of auxiliary sources	en
dc.subject.other	Numerical solution	en
dc.subject.other	Sinusoidal currents	en
dc.subject.other	Thin-wire antennas	en
dc.subject.other	Two equation	en
dc.subject.other	Wire antennas	en
dc.subject.other	Antenna feeders	en
dc.subject.other	Galerkin methods	en
dc.subject.other	Integral equations	en
dc.subject.other	Wire	en
dc.subject.other	Antennas	en
dc.title	On the oscillations appearing in numerical solutions of solvable and nonsolvable integral equations for thin-wire antennas	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/TAP.2010.2044319	en
heal.identifier.secondary	5422615	en
heal.identifier.secondary	http://dx.doi.org/10.1109/TAP.2010.2044319	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	Differences between certain solvable and nonsolvable ill-posed integral equations, with the same nonsingular kernel, are discussed. The main results come from constructing a solvable equation in the context of straight thin-wire antennas. The kernel of this equation is the usual approximate (also called reduced) kernel, while its exact solution is the familiar sinusoidal current. Numerical solutions to this solvable equation are compared to corresponding numerical solutions of the usualHalln and Pocklingtonequations with the approximate kernel; it is known from previous publications that these last two equations are nonsolvable and that their numerical solutions present severe oscillations when the number of basis functions is sufficiently large. It is found that the difficulties encountered in the former (solvable) equation are much less important compared to those of the nonsolvable ones. The same conclusion is brought out from other integral equations, arising in different contexts (thin-wire circular-loop antenna, Method of Auxiliary Sources, and straight wire antenna of infinite length). We discuss the consistency of our results with Picard's theorem. The results in this paper supplement previous publications regarding the difficulties of numerically solving thin-wire integral equations with the approximate kernel. © 2006 IEEE.	en
heal.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC	en
heal.journalName	IEEE Transactions on Antennas and Propagation	en
dc.identifier.doi	10.1109/TAP.2010.2044319	en
dc.identifier.isi	ISI:000277339900022	en
dc.identifier.volume	58	en
dc.identifier.issue	5	en
dc.identifier.spage	1635	en
dc.identifier.epage	1644	en