Dispersion and pollution of meshless solutions for the Helmholtz equation Original Research Article

It is well known today that the standard finite element method (FEM) is unreliable to compute approximate solutions of the Helmholtz equation for high wavenumbers due to the pollution effect, consisting mainly of the dispersion, i.e. the numerical wavelength is longer than the exact one. Unless highly refined meshes are used, FEM solutions lead to unacceptable solutions in terms of precision, while the use of very refined meshed increases the cost 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 comparison with the stabilized FEM. Moreover, the present meshless formulation 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 accuracy of the numerical results w.r. FEM results.