TITLE

# Dispersion free analysis of acoustic problems using the alpha finite element method

AUTHOR(S)
He, Z. C.; Liu, G. R.; Zhong, Z. H.; Zhang, G. Y.; Cheng, A. G.
PUB. DATE
November 2010
SOURCE
Computational Mechanics;Nov2010, Vol. 46 Issue 6, p867
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
The classical finite element method (FEM) fails to provide accurate results to the Helmholtz equation with large wave numbers due to the well-known â€œpollution errorâ€ caused by the numerical dispersion, i.e. the numerical wave number is always smaller than the exact one. This dispersion error is essentially rooted at the â€œoverly-stiffâ€ feature of the FEM model. In this paper, an alpha finite element method (Î±-FEM) is then formulated for the acoustic problems by combining the â€œsmaller wave numberâ€ model of FEM and the â€œlarger wave numberâ€ model of NS-FEM through a scaling factor $${a\in [0,1]}$$ . The motivation for this combined approach is essentially from the features of â€œoverly-stiffâ€ FEM model and â€œoverly-softâ€ NS-FEM model, and accurate solutions can be obtained by tuning the Î±-FEM model. A technique is proposed to determine a particular alpha with which the Î±-FEM model can possess a very â€œclose-to-exactâ€ stiffness, which can effectively reduce the dispersion error leading to dispersion free solutions for acoustic problems. Theoretical and numerical studies shall demonstrate the excellent properties of the present Î±-FEM.
ACCESSION #
52926275

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