Accurate acoustic computations using a meshless method

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Accurate acoustic computations using a meshless method

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. The paper presents an application of the Element-Free Galerkin Method (EFGM) leading to extremely accurate results in comparison with the FEM. Moreover, the present meshless formulation is not restricted to regular distribution of nodes as some stabilisation methods and a simple but real-life problem is investigated in order to show the improvement in the accuracy of the numerical results, as compared with FEM results.SCOPUS: cp.jinfo:eu-repo/semantics/publishe

Element-free Galerkin solutions for Helmholtz problems: Formulation and numerical assessment of the pollution effect

The Element-Free Galerkin Method (EFGM), a particular case of the meshless methods, is examined in its application to acoustic wave propagation addressed by the Helmholtz equation. Dispersion and pollution effects, two problems encountered by the classical numerical methods, are reviewed. Numerical tests on two-dimensional problems focus on the parameters governing the formulation of the EFGM. They also demonstrate that the EFGM is affected by dispersion and pollution effects as well as FEM, but these effects are rather low, showing that the EFGM is a promising method. © 1998 Elsevier Science S.A. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Optimized meshless method for acoustics

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Méthode d'approximation nodale en acoustique et analyse de l'erreur de dispersion

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Numerical computation of waves: a meshless alternative

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A 2D meshless method for acoustics

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Methode d'approximation nodale optimisee pour l'acoustique

The element-free Galerkin method is formulated for the Helmholtz problem. It is based on a moving least square method. This article shows that it is possible to determine the speed of propagation of the numerical wave and to tune the parameters of the method in order to minimise the dispersion.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Dispersion and pollution of meshless solutions for the Helmholtz equation

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.info:eu-repo/semantics/publishe

Dispersion analysis for the element-free Galerkin method

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