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 applicabil- ity of MAS may be restricted by issues concerning the divergence of the auxiliary currents, manifested by the appearance of exponentially large os- cillations. 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 prop- erly 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.

翻译：零场方法(NFM)和辅助源方法(MAS)已被广泛应用于涉及波传播与散射的各类边值问题数值求解。研究表明，在某些条件下，MAS的适用性可能因辅助电流发散问题而受到限制，具体表现为指数级大幅振荡的出现。本文结合NFM与表面等效原理(SEP)，以介质圆柱（内/外）线源激励问题为参考，解析研究了NFM-SEP组合方法的收敛特性。我们主要目标是证明：与MAS相反，经恰当归一化的离散NFM-SEP电流始终收敛于对应的连续电流密度，因此不会出现发散和振荡现象。NFM-SEP的理论分析辅以与MAS的详细对比及典型数值结果说明结论。