Element-Free Galerkin Method formulation for acoustic analyses: rationale and strategy

摘要

This paper deals with the numerical simulation of the acoustic wave propagation. It is well known today that the standard finite element method (FEW) 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 two dimensions. 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. However, to lead to those very accurate results for 1-D and 2-D problems, the EFGM needs an important computational time, mainly due to the computation and the assembly of the stiffness and mass matrices. Thus, in order to reduce this computational time, it is suggested in this paper, as a first step, to take advantage from the developments of computer hardware, currently moving towards multi-processor machines, by computing and assemblying the matrices simultaneously on several processors. This is called a parallel assembly algorithm. The paper presents the numerical assessment of the CPU performance of the parallel implementation vs the sequential one.