Dispersion analysis of the meshless local boundary integral equation and radial basis integral equation methods for the Helmholtz equation

Abstract

Numerical solutions of the Helmholtz equation suffer from pollution effect especially for higher wavenumbers. The major cause for this is the dispersion error which is defined as the relative phase difference between the numerical solution of the wave and the exact wave. The dispersion error for the meshless methods can be a priori determined at an interior source node assuming that the potential field obeys a harmonic evolution with the numerical wavenumber.In this paper, the dispersion errors, in the solution of 2D Helmholtz equation, for two different meshless methods are investigated, the local boundary integral equation method and the radial basis integral equation method. Radial basis functions, with second order polynomials and frequency-dependent polynomial basis vectors are used for the interpolation of the potential field in both methods. The results have been found to be of comparable accuracy with other meshless approaches reported in the literature.