Accurate acoustic computations using a meshless method

  • Stéphane Suleau Université Libre de Bruxelles
  • Philippe Bouillard Université Libre de Bruxelles

Abstract

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.

Keywords

References

[1] I. Babuška, F. Ihlenburg, E. Paik and S. Sauter. A Generalized Finite Element Method for solving the Helmholtz equation in two dimensions with minimal pollution. Comput. Methods Appl. Mech. Eng., 128: 325- 359, 1995.
[2] I. Babuška, F. Ihlenburg, T. Strouboulis, S.K. Gangaraj. A posteriori error estimation for finite element solutions of Helmholtz' equation. Part I: The quality of local indicators and estimators. Int. J. Numer. Methods Eng. , 40: 3443- 3462, 1997.
[3] I. Babuška, J.M. Melenk. The partition of unity method. Int. J. Numer. Methods Eng., 40: 727- 758, 1997. [4] T . Belytschko, Y. Krongauz, D. Organ, M. Fleming, P. Krysl. Meshless methods: An overview and recent developments. Comput. Methods Appl. Mech. Eng. , 139: 3- 47, 1996.
[5] T . Belytschko, Y.Y. Lu, L. Gu, Element-free Galerkin methods. Int. J. Numer. Methods Eng., 37: 229- 256, 1994.
Published
Mar 24, 2023
How to Cite
SULEAU, Stéphane; BOUILLARD, Philippe. Accurate acoustic computations using a meshless method. Computer Assisted Methods in Engineering and Science, [S.l.], v. 8, n. 2-3, p. 455-468, mar. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1188>. Date accessed: 13 nov. 2024.
Section
Articles