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Title: Dispersion free analysis of acoustic problems using the alpha finite element method
Authors: He, Z.C.
Liu, G.R. 
Zhong, Z.H.
Zhang, G.Y.
Cheng, A.G.
Keywords: Acoustic
Alpha finite element method (α-FEM)
Finite element method (FEM)
Meshfree method
Numerical error
Numerical method
Issue Date: Nov-2010
Citation: He, Z.C., Liu, G.R., Zhong, Z.H., Zhang, G.Y., Cheng, A.G. (2010-11). Dispersion free analysis of acoustic problems using the alpha finite element method. Computational Mechanics 46 (6) : 867-881. ScholarBank@NUS Repository.
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 "pollution error" 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 "overly-stiff" feature of the FEM model. In this paper, an alpha finite element method (α-FEM) is then formulated for the acoustic problems by combining the "smaller wave number" model of FEM and the "larger wave number" model of NS-FEM through a scaling factor {∈ [0,1]}. The motivation for this combined approach is essentially from the features of "overly-stiff" FEM model and "overly-soft" NS-FEM model, and accurate solutions can be obtained by tuning the α-FEM model. A technique is proposed to determine a particular alpha with which the α-FEM model can possess a very "close-to-exact" 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 α-FEM. © 2010 Springer-Verlag.
Source Title: Computational Mechanics
ISSN: 01787675
DOI: 10.1007/s00466-010-0516-y
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