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

Abstract

The radial basis function generatedfinite difference (RBFFD) method is applied to the analysis of homogenous waveguides. To this end, the Helmholtz equation and the bound ary conditions are collocated on the waveguide cross section. At each collocation node, derivatives are locally approximated by RBFFD formulas based on polyharmonic splines supplemented with highdegree 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 waveguides.

Generalized Finite Difference Method for Solving Waveguide Eigenvalue Problems

“…Figure 6 shows the distribution of computational nodes on the cross section of the eccentric circular waveguide when solving even TM modes. As shown in Table 2, the results of traditional GFDM and improved GFDM agree with the results given in [5].…”

“…When dealing with complex structures or discontinuous boundaries, these grid-based methods suffer from the problem of complex meshing and low accuracy. The radial basis function (RBF) interpolation method is a meshless method, and its main idea is to use basis functions to approximate the function to be sought over the entire simulation domain [5]. By requiring that the approximate value and actual value are strictly equal, a matrix equation with weight coefficients as variables is constructed, and the derivative at the center node is transformed into a linear combination of the function values of the surrounding nodes.…”

“…Normalized cutoff wavenumber for the first six even TM modes Traditional GFDM Improved GFDM Method in[5] …”