Convergence and oscillations in the method of auxiliary sources

When applying the method of auxiliary sources (MAS) one seeks to satisfy the boundary condition on N discrete points on a perfect electric conductor (PEC) by using N auxiliary sources located inside the PEC surface. The first purpose of this work is to show, through an analytical study that, in the limit of an infinite number of sources, it is possible to have a convergent MAS field together with divergent MAS currents. The important feature of our study is that MAS currents and fields can be found explicitly for finite N and that the explicit solutions are simple enough to be studied asymptotically in the limit N rarr infin. The second purpose of this work is to discuss the nature of the divergent currents using asymptotic methods: We show that, as a result of the divergence, the MAS currents oscillate very rapidly. Certain similarities to the null-field method are mentioned.