On two types of convergence in the method of auxiliary sources

Fikioris, G

dc.contributor.author	Fikioris, G	en
dc.date.accessioned	2014-03-01T01:24:48Z
dc.date.available	2014-03-01T01:24:48Z
dc.date.issued	2006	en
dc.identifier.issn	0018-926X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17444
dc.subject	Convergence of numerical methods	en
dc.subject	Fredholm integral equations	en
dc.subject	Scattering	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.classification	Telecommunications	en
dc.subject.other	Approximation theory	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Electromagnetic field measurement	en
dc.subject.other	Electromagnetic wave scattering	en
dc.subject.other	Integration	en
dc.subject.other	Problem solving	en
dc.subject.other	Fredholm integral equations	en
dc.subject.other	Method of auxiliary sources	en
dc.subject.other	Perfect electric conductor	en
dc.subject.other	Electromagnetic wave propagation	en
dc.title	On two types of convergence in the method of auxiliary sources	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/TAP.2006.877171	en
heal.identifier.secondary	http://dx.doi.org/10.1109/TAP.2006.877171	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	The method of auxiliary sources (MAS) is often applied to problems involving an externally illuminated, smooth, perfect electric conductor (PEC). One seeks to approximately satisfy the boundary condition on the PEC surface using N auxiliary sources located inside the PEC surface. Usually, the underlying auxiliary surface is also smooth and closed. The currents on the auxiliary sources (""MAS currents"") are the initial unknowns; once they have been found, one can easily determine the field due to them (""MAS field"") at all points external to the auxiliary surface and, in particular, at all points external to the PEC scatterer. We show that, in the limit N → ∞, it is possible to have a convergent MAS field together with divergent MAS currents, and that this phenomenon is accompanied by an abrupt behavior of the limiting value of the MAS field. We show this possibility through an analytical study of a two-dimensional scattering problem involving a circular cylinder, in which MAS fields and currents can be determined explicitly. The analytical study proceeds from first principles; it involves fundamental electromagnetics and relatively simple mathematical manipulations. Numerical results supplement the analytical study and demonstrate the nature of the aforementioned divergence. Our study sheds light on other aspects of MAS; in particular, it establishes interesting similarities and differences between MAS and its ""continuous version,"" and reveals many similarities between MAS currents and numerical solutions of Hallén's integral equation 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.2006.877171	en
dc.identifier.isi	ISI:000238866000014	en
dc.identifier.volume	54	en
dc.identifier.issue	7	en
dc.identifier.spage	2022	en
dc.identifier.epage	2033	en