On the phenomenon of oscillations in the method of auxiliary sources

Fikioris, G; Psarros, I

dc.contributor.author	Fikioris, G	en
dc.contributor.author	Psarros, I	en
dc.date.accessioned	2014-03-01T01:26:48Z
dc.date.available	2014-03-01T01:26:48Z
dc.date.issued	2007	en
dc.identifier.issn	0018-926X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18226
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	Circular cylinders	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Electric conductors	en
dc.subject.other	Electric currents	en
dc.subject.other	Errors	en
dc.subject.other	Integral equations	en
dc.subject.other	Convergent field	en
dc.subject.other	Ground plane	en
dc.subject.other	Scattering problems	en
dc.subject.other	Circuit oscillations	en
dc.title	On the phenomenon of oscillations in the method of auxiliary sources	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/TAP.2007.895621	en
heal.identifier.secondary	http://dx.doi.org/10.1109/TAP.2007.895621	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	When one applies the method of auxiliary sources to scattering problems involving perfect conductors, one first seeks fictitious auxiliary currents located inside the conductor, and then determines the field from these currents. For a simple two-dimensional problem involving an infinite circular cylinder illuminated by an electric current filament, it has recently been shown analytically that it is possible to have divergent auxiliary currents (to make this statement precise, one must properly normalize the currents), together with a convergent field. It was also shown - through numerical investigations - that the aforementioned divergence appears as abnormal, rapid oscillations. In the present paper, we investigate such phenomena in more detail, with particular emphasis on oscillations. For a perfectly conducting ground plane illuminated by an electric current filament, we once again demonstrate the possibility of having divergent, oscillating currents producing a convergent field. We develop an asymptotic formula for the oscillating current values, which sheds light on the nature of the oscillations. We revisit the circular-cylinder problem to develop a similar asymptotic formula. We also discuss roundoff errors, and possible generalizations to scatterers of other shapes. The present study is to a great extent analytical, with the analytical predictions confirmed and supplemented by numerical results. © 2007 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.2007.895621	en
dc.identifier.isi	ISI:000246535100010	en
dc.identifier.volume	55	en
dc.identifier.issue	5	en
dc.identifier.spage	1293	en
dc.identifier.epage	1304	en