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A mass-redistributed finite element method (MR-FEM) for acoustic problems using triangular mesh
- Source :
- Journal of Computational Physics. 323:149-170
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
Abstract
- 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.
- Subjects :
- Numerical Analysis
Mathematical optimization
Physics and Astronomy (miscellaneous)
Discretization
Applied Mathematics
Numerical analysis
02 engineering and technology
Mixed finite element method
Mass matrix
01 natural sciences
Finite element method
Computer Science Applications
010101 applied mathematics
Computational Mathematics
020303 mechanical engineering & transports
0203 mechanical engineering
Mesh generation
Modeling and Simulation
Triangle mesh
Applied mathematics
0101 mathematics
Conservation of mass
Mathematics
Subjects
Details
- ISSN :
- 00219991
- Volume :
- 323
- Database :
- OpenAIRE
- Journal :
- Journal of Computational Physics
- Accession number :
- edsair.doi...........ed110ac3aebc38af75ea26dbe9ec5cb0