The radial basis function-generated-finite-difference (RBF-FD) method is applied to the analysis of homogenous waveguides. To this end, the Helmholtz equation and the boundary conditions are collocated on the waveguide cross section. At each collocation node, derivatives are locally approximated by the RBF-FD formulas based on the polyharmonic splines supplemented with high-degree polynomials. As a result, a sparse matrix eigenvalue problem is obtained, which allows cutoff wavenumbers and axial fields to be calculated. To illustrate the accuracy of the method, we consider a semicircular and an eccentric circular waveguide.

中文翻译：

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通过无网格径向基函数生成有限差分法分析均匀波导

径向基函数生成有限差分 (RBF-FD) 方法应用于同质波导的分析。为此，亥姆霍兹方程和边界条件被配置在波导截面上。在每个搭配节点，导数由 RBF-FD 公式局部逼近，该公式基于辅以高次多项式的多调和样条。结果，得到了一个稀疏矩阵特征值问题，它允许计算截止波数和轴向场。为了说明该方法的准确性，我们考虑一个半圆形和一个偏心圆形波导。