Acoustic simulation using α-FEM with a general approach for reducing dispersion error

Z. C. He, Eric Li, G. Y. Li, F. Wu, G. R. Liu, X. Nie

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The alpha finite element method (α-FEM) developed recently has showed outstanding features in solving solid mechanics and acoustic problems. In the α-FEM, a parameter alpha has been introduced to make the best use of "over-stiffness" of the FEM model and "over-softness" of the NS-FEM model to achieve the ultimate performance. Because the parameter alpha varies with the problems and the mesh size, it is difficult to find a general approach to determine, which holds back the application of the α-FEM method. In this paper, acoustic simulation using α-FEM with a general approach for reducing dispersion error is proposed. We first carry out a theoretical analysis of dispersion error, leading to a very important relation between the dispersion error and the parameter alpha. Next, the parameter of alpha is then determined by minimizing the dispersion error. The determined parameter alpha enables a proper gradient smoothing operation in the α-FEM, and provides a perfect balance between the stiffness and mass in the discrete system matrix, which dramatically reduces the dispersion error. The properties of the present α-FEM have been confirmed numerically via examples of 1D, 2D and 3D acoustic problems with various boundary conditions.

Original languageEnglish
Pages (from-to)241-253
Number of pages13
JournalEngineering Analysis with Boundary Elements
Volume61
DOIs
Publication statusPublished - 29 Dec 2015

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