A mass-redistributed finite element method (MR-FEM) for acoustic problems using triangular mesh

JOURNAL OF COMPUTATIONAL PHYSICS

卷:323

Article

He, Z. C.^1,2  Li, Eric^1,3  Liu, G. R.⁴  Li, G. Y.^1,2  Cheng, A. G.^1,2 

[1] Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha 410082, Hunan, Peoples R China

[2] Joint Ctr Intelligent New Energy Vehicle, Shanghai 201804, Peoples R China

[3] Chinese Univ Hong Kong, Dept Mech & Automat Engn, Shatin, Hong Kong, Peoples R China

[4] Univ Cincinnati, Sch Aerosp Syst, Cincinnati, OH 45221 USA

关键词: Acoustic;    Numerical method;    Mass-redistributed finite element method (MR-FEM);    Dispersion error;   

DOI  :  10.1016/j.jcp.2016.07.025

来源: Elsevier

【 摘 要 】

The accuracy of numerical results using standard finite element method (FEM) in acoustic problems will deteriorate with increasing frequency due to the dispersion error. Such dispersion error depends on the balance between the stiffness and mass of discretization equation systems. This paper reports an improved finite element method (FEM) for solving acoustic problems by re-distributing the mass in the mass matrix to tune the balance, aiming to minimize the dispersion errors. This is done by shifting the integration point locations when computing the entries of the mass matrix, while ensuring the mass conservation. The new method is verified through the detailed numerical error analysis, and a strategy is also proposed for the best mass redistribution in terms of minimizing dispersion error. The relative dispersion error of present mass-redistributed finite element method (MR-FEM) is found to be much smaller than the FEM solution, in both theoretical prediction and numerical examination. The present MR-FEM works well by using the linear triangular elements that can be generated automatically, which enables automation in computation and saving computational cost in mesh generation. Numerical examples demonstrate the advantages of MR-FEM, in comparison with the standard FEM using the same triangular meshes and quadrilateral meshes. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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