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.

中文翻译：

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零场法的基础知识 - 介电圆柱体散射的表面等效原理方法


零场法 (NFM) 和辅助源法 (MAS) 均已广泛用于涉及波传播和散射的各种应用中出现的边值问题的数值求解。已经表明，在某些条件下，MAS 的适用性可能会受到辅助电流发散问题的限制，表现为指数级大振荡的出现。在这项工作中，我们将 NFM 与表面等效原理 (SEP) 结合起来，并参考介电圆柱体的（内部或外部）线源激励问题，分析研究了组合 NFM-SEP 的收敛特性。我们的主要目的是证明（与 MAS 相反）离散 NFM-SEP 电流在适当归一化时始终收敛于相应的连续电流密度，因此不会出现发散和振荡现象。 NFM-SEP 的理论分析伴随着与 MAS 的详细比较以及说明结论的代表性数值结果。