Convergent Fields Generated by Divergent Currents in the Method of Auxiliary Sources

  • George FikiorisEmail author
  • Nikolaos L. Tsitsas
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 99)


A very simple scattering problem is considered, together with its solution obtained via the Method of Auxiliary Sources (MAS). We show that it is possible to concurrently have divergence of the auxiliary currents together with convergence of the scattered field generated by these divergent currents. The divergence manifests itself as rapid, unphysical oscillations in the auxiliary currents. It is stressed that the oscillations are not due to effects such as roundoff, matrix ill-conditioning, or to the well-studied phenomenon of internal resonances. We arrive at our conclusions using a number of means including asymptotic methods and a thorough discussion of the singularities of the analytic continuation of the scattered field. We also make a detailed comparison to corresponding discretizations of the Extended Integral Equation (EIE), in which similar phenomena do not occur. Analogies to superdirectivity and extensions to more complicated geometries are pointed out.


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Authors and Affiliations

  1. 1.School of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece
  2. 2.Department of InformaticsAristotle University of ThessalonikiThessalonikiGreece

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