One-dimensional dispersion analysis for the element-free Galerkin method for the Helmholtz equation

The standard finite element method (FEM) is unreliable to compute approxima te solutions of the Helmholtz equation for high wave numbers due to the dis persion, unless highly refined meshes are used, leading to unacceptable res olution times. The paper presents an application of the element-free Galerk in method (EFG) and focuses on the dispersion analysis in one dimension. It shows that, if the basis contains the solution of the homogenized Helmholt z equation, it is possible to eliminate the dispersion in a very natural wa y while it is not the case for the finite element methods. For the general case, it also shows that it is possible to choose the parameters of the met hod in order to minimize the dispersion. Finally, theoretical developments are validated by numerical experiments showing that, for the same distribut ion of nodes, the element-free Galerkin method solution is much more accura te than the finite element one. Copyright (C) 2000 John Wiley & Sons, Ltd.