Dispersion and pollution of meshless solutions for the Helmholtz equation

It is well known today that the standard finite element method (FEM) is unr eliable to compute approximate solutions of the Helmholtz equation for high wavenumbers due to the pollution effect, consisting mainly of the dispersi on, i.e. the numerical wavelength is longer than the exact one. Unless high ly refined meshes are used, FEM solutions lead to unacceptable solutions in terms of precision, while the use of very refined meshed increases the cos t in terms of computational times. The paper presents an application of the element-free Galerkin method (EFGM) and focuses on the dispersion analysis in 2D. It shows that it is possible to choose the parameters of the method in order to minimize the dispersion and to get extremely good results in c omparison with the stabilized FEM. Moreover, the present meshless formulati on is not restricted to regular distribution of nodes and a simple but real -life problem is investigated in order to show the improvement in the accur acy of the numerical results w.r. FEM results. (C) 2000 Elsevier Science S. A. All rights reserved.