Acoustic simulation using α-FEM with a general approach for reducing dispersion error. (December 2015)

• Record Type: Journal Article
• Authors: He, Z.C.; Li, Eric; Li, G.Y.; Wu, F.; Liu, G.R.; Nie, X.
• Is Part Of: Engineering analysis with boundary elements. Volume 61(2015:Dec.)
• Page Start: 241
• Page End: 253
• Publication Date: 2015-12
• Subjects: Numerical method -- Alpha finite element method (α-FEM) -- Smoothed finite element methods -- Gradient smoothing operation -- Acoustics -- Dispersion error; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2015.07.018
• Languages: English
• ISSNs: 0955-7997

Abstract

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.