Meshless time domain methods allow flexible distribution of nodes in the computational domain. The radial point interpolation method (RPIM) in electromagnetics with Gaussian radial basis functions (RBFs) requires global interpolation matrices with large condition numbers even for simple problems such as eigenvalue analysis of a circular waveguide. In addition, nonorthogonal grids in such problems demand divergence-free conditions to be enforced. In this letter, a divergence-free inverse multiquadric RBF has been proposed to efficiently solve such electromagnetic (EM) problems. Real parts in eigenvalues are nearly eliminated by this approach, thus removing spurious solutions. In addition, the proposed approach results in longtime stability of numerical analysis.

中文翻译：

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使用径向点插值法的圆形波导特征值分析中的逆多二次径向基函数

无网格时域方法允许在计算域中灵活分布节点。具有高斯径向基函数 (RBF) 的电磁学中的径向点插值法 (RPIM) 需要具有大条件数的全局插值矩阵，即使对于圆形波导的特征值分析等简单问题也是如此。此外，此类问题中的非正交网格需要强制执行无发散条件。在这封信中，提出了一种无散度的逆多二次 RBF 来有效地解决此类电磁 (EM) 问题。这种方法几乎消除了特征值中的实部，从而消除了伪解。此外，所提出的方法导致数值分析的长期稳定性。