The method of auxiliary sources (MAS) is an established technique for the numerical solution of electromagnetic shielding and scattering problems exhibiting an increasing interest for the simulation of various electromagnetic compatibility (EMC) applications. In previous works, it was shown that for the problem of transverse magnetic illumination of a perfect electric conducting cylinder by an electric current filament, it is possible for large numbers $N$ of auxiliary sources that the MAS currents diverge and oscillate, while the generated MAS field converges to the exact solution. In this article, we further analyze the convergence issues and oscillations encountered in the MAS by considering the transverse electric case due to excitation by a magnetic current filament. We demonstrate analytically that the convergence/divergence phenomena of the currents and fields also occur in this problem and then study the nature of this divergence in detail. In particular, we prove a large- $N$ asymptotic formula for the divergent MAS currents, which captures accurately the important characteristics of the associated inherent oscillations. Numerical results for noncircular shapes are also presented. The discussed effects must be carefully taken into account in EMC simulations pertaining to cylindrical conductors.

中文翻译：

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PEC筒散射辅助源法电流场收敛分析


辅助源方法 (MAS) 是一种用于电磁屏蔽和散射问题数值求解的成熟技术，对各种电磁兼容性 (EMC) 应用的仿真表现出越来越大的兴趣。在之前的工作中，已经表明，对于电流灯丝对完美导电圆柱体的横向磁照明问题，大量$N$的辅助源可能导致MAS电流发散和振荡，同时产生MAS 场收敛到精确解。在本文中，我们通过考虑磁流灯丝激励引起的横向电情况，进一步分析了 MAS 中遇到的收敛问题和振荡。我们通过分析证明了该问题中也会出现电流和场的收敛/发散现象，然后详细研究这种发散的本质。特别是，我们证明了发散 MAS 电流的大$N$ 渐近公式，该公式准确地捕获了相关固有振荡的重要特征。还提供了非圆形形状的数值结果。在与圆柱形导体相关的 EMC 仿真中必须仔细考虑所讨论的影响。