Mesh-free approach to Hemholtz equation based on radial basis functions

Recently, a radial basis functions (RBFs) method, which was originally proposed for interpolation problems, has been developed and applied to solve partial differential equations and eigenproblems. Properties of that method (mesh-free algorithm) allows one to use it in many areas, including electromagnetics. In this paper the mesh-free RBF method for solving Helmholtz equation was applied and a new adaptive algorithm for defining the set of interpolation centers was proposed. Using the proposed approach the cutoff wavelengths and the field distribution in cylindrical waveguides of arbitrary cross-section were calculated with a high accuracy.