On the Nature of Oscillations in Discretizations of the Extended Integral Equation

Using analytical methods, previous studies have shown that it is possible for oscillations to occur in the auxiliary surface current determined by applying the method of auxiliary sources (MAS) to problems of scattering by perfect conductors of a very simple shape. Such oscillations are inherent to MAS and would occur even in a hypothetical computer with ideal hardware and software. Because the integral equation relevant to MAS very much resembles the “extended integral equation” (in which the unknown is the actual surface current on the conductor), one might surmise that similar oscillations also occur in discretizations of the latter equation. In this communication, we use analytical means to show that this is not the case. Therefore, any oscillations that do occur in discretizations of the extended integral equation are-at least for “sufficiently simple” problems-likely to be due to matrix ill-conditioning, which magnifies errors that would otherwise be unimportant.