On the Deviation of MAS Fields in the Far-Field Region of Elementary Sources Close to Infinite Boundaries

For the simple problem of an electric current filament close to a perfectly conducting infinite plane, the method of auxiliary sources (MAS) yields numerical solutions that are systematically deviating from the exact one beyond a certain horizontal distance (i.e., outside the region demarcated by the finite set of auxiliary sources). In this article, in order to shed light on the edge-effect nature of the aforementioned discrepancy, also arising in more complex problems, this issue is investigated both numerically and asymptotically through an infinite version of MAS, which assumes an infinite number of auxiliary sources. The analysis is followed by discussions on the uniqueness of the exact solution and the adequacy/suitability of certain error metrics as quality and reliability indicators of MAS results.