The method of auxiliary sources (MAS) is one of the numerical methods employed for the determination of the cutoff wavenumbers (eigenvalues) of cylindrical waveguides. According to the general scheme of MAS, the eigenvalues are obtained by requiring the square impedance matrix to be singular and therefore its determinant to be zero (or its condition number to be large). For large matrices, such computations are complicated and time-consuming. Additionally, these schemes are frequently contaminated with spurious eigenvalues. To overcome the difficulties, an efficient method based on MAS along with an excitation source has been proposed. The eigenvalues are obtained by measuring the physical response of the waveguide's domain to this source; thus, an interior problem is always solved. This article is a comprehensive presentation of this method and its variants and aims to emphasize fundamental and often unfamiliar attributes. One of the main objectives is to show analytically and numerically that when an internal source is used, the eigenvalues are accurately computed without employing a regularization procedure. The method is applied to hollow simply and multiply connected waveguides with circular, elliptical, and rounded-triangular cross sections. The results are compared with those obtained from COMSOL Multiphysics. Moreover, the phenomenon of divergent and oscillating MAS currents-which may or may not occur depending on the relative position between the auxiliary curve and the excitation source-is discussed. It is emphasized that, with proper care, the phenomenon does not affect the accurate computation of the eigenvalues.

中文翻译：

---

带激励源的辅助源法模态分析


辅助源法（MAS）是用于确定圆柱形波导截止波数（特征值）的数值方法之一。根据MAS的一般方案，特征值是通过要求方阻抗矩阵是奇异的并且因此其行列式为零（或者其条件数很大）来获得的。对于大型矩阵，这种计算既复杂又耗时。此外，这些方案经常受到虚假特征值的污染。为了克服这些困难，提出了一种基于 MAS 和激励源的有效方法。通过测量波导域对此源的物理响应来获得特征值；因此，内部问题总能得到解决。本文全面介绍了该方法及其变体，旨在强调基本且通常不熟悉的属性。主要目标之一是通过分析和数值方式表明，当使用内部源时，无需采用正则化程序即可准确计算特征值。该方法适用于具有圆形、椭圆形和圆角三角形横截面的空心简单波导和多重连接波导。结果与 COMSOL Multiphysics 获得的结果进行了比较。此外，还讨论了 MAS 电流发散和振荡的现象，这种现象可能发生也可能不发生，具体取决于辅助曲线和激励源之间的相对位置。需要强调的是，只要小心谨慎，这种现象不会影响特征值的精确计算。