Dispersion and pollution of the cell-based smoothed radial point interpolation method (CS-RPIM) solution for the Helmholtz equation

Abstract

Abstract The standard finite element method (FEM) is unreliable to compute approximate solutions of the Helmholtz equation for high wave numbers due to the dispersion. This paper presents an application of the cell-based smoothed radial point interpolation method (CS-RPIM) and focuses on the dispersion analysis in two-dimensional (2D) Helmholtz problems. The dispersion error is mainly caused by the ‘overly stiff’ feature of the discrete model. Therefore a properly “softened” stiffness for the discrete model is much more essential to the root of the numerical dispersion error. Owing to the proper softening effects provided by the cell-based gradient smoothing operations, the CS-RPIM model, therefore, can significantly reduce the dispersion error in the numerical solution. Numerical results demonstrated that, the CS-RPIM yields considerably better results than the FEM and EFGM, because of the crucial effectiveness in handling dispersion.