Convergence and 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	2014-03-01T02:45:12Z
dc.date.available	2014-03-01T02:45:12Z
dc.date.issued	2008	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32204
dc.subject	Convergence of numerical methods	en
dc.subject	Fredholm integral equations	en
dc.subject	Scattering	en
dc.subject.other	Circular cylinders	en
dc.subject.other	Cylinders (shapes)	en
dc.subject.other	Electric current measurement	en
dc.subject.other	Electric fields	en
dc.subject.other	Electric power supplies to apparatus	en
dc.subject.other	Filaments (lamp)	en
dc.subject.other	Motion estimation	en
dc.subject.other	Numerical analysis	en
dc.subject.other	Current filaments	en
dc.subject.other	Electromagnetic theories	en
dc.subject.other	Fredholm integral equations	en
dc.subject.other	Mathematical methods	en
dc.subject.other	Scattering	en
dc.subject.other	Convergence of numerical methods	en
dc.title	Convergence and oscillations in the method of auxiliary sources	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1109/MMET.2008.4580896	en
heal.identifier.secondary	4580896	en
heal.identifier.secondary	http://dx.doi.org/10.1109/MMET.2008.4580896	en
heal.publicationDate	2008	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 also discuss roundoff errors. The present study is to a great extent analytical, with the analytical predictions confirmed and supplemented by numerical results. © 2008 IEEE.	en
heal.journalName	Mathematical Methods in Electromagnetic Theory, MMET, Conference Proceedings	en
dc.identifier.doi	10.1109/MMET.2008.4580896	en
dc.identifier.spage	53	en
dc.identifier.epage	58	en