  The null-field method (NFM) and the method of auxiliary sources (MAS) have
been both used extensively for the numerical solution of boundary-value
problems arising in diverse applications involving propagation and scattering
of waves. It has been shown that, under certain conditions, the applicability
of MAS may be restricted by issues concerning the divergence of the auxiliary
currents, manifested by the appearance of exponentially large oscillations. In
this work, we combine the NFM with the surface equivalence principle (SEP) and
investigate analytically the convergence properties of the combined NFM-SEP
with reference to the problem of (internal or external) line-source excitation
of a dielectric cylinder. Our main purpose is to prove that (contrary to the
MAS) the discrete NFM-SEP currents, when properly normalized, always converge
to the corresponding continuous current densities, and thus no divergence and
oscillations phenomena appear. The theoretical analysis of the NFM-SEP is
accompanied by detailed comparisons with the MAS as well as with representative
numerical results illustrating the conclusions.
