Analysis of Homogeneous Waveguides via the Meshless Radial Basis Function-Generated-Finite-Difference Method

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.