Solving helmholtz equation by meshless radial basis functions method

Abstract

In this paper, we propose a brief and general process to compute the eigenvalue of arbitrary waveguides using meshless method based on radial basis functions (MLM-RBF) interpolation. The main idea is that RBF basis functions are used in a point matching method to solve the Helmholtz equation only in Cartesian system. Two kinds of boundary conditions of waveguide problems are also analyzed. To verify the efficiency and accuracy of the present method, three typical waveguide problems are analyzed. It is found that the results of various waveguides can be accurately determined by MLM-RBF.