Diagonal Form Fast Multipole Boundary Element Method for 2D Acoustic Problems Based on Burton-Miller BIE Formulation and Its Applications

WU Hai-jun; JIANG Wei-kang; LIU Yi-jun

doi:10.3879/j.issn.1000-0887.2011.08.003

Volume 32 Issue 8

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WU Hai-jun, JIANG Wei-kang, LIU Yi-jun. Diagonal Form Fast Multipole Boundary Element Method for 2D Acoustic Problems Based on Burton-Miller BIE Formulation and Its Applications[J]. Applied Mathematics and Mechanics, 2011, 32(8): 920-933. doi: 10.3879/j.issn.1000-0887.2011.08.003

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Diagonal Form Fast Multipole Boundary Element Method for 2D Acoustic Problems Based on Burton-Miller BIE Formulation and Its Applications

doi: 10.3879/j.issn.1000-0887.2011.08.003

1.
State Key Laboratory of Machinery System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;

Received Date: 2010-06-10
Rev Recd Date: 2011-05-10
Publish Date: 2011-08-15

Abstract

Abstract

The formulations and implementation of the fast multipole BEM (FMBEM) for 2D acoustic problems were described indetail.The kernel function expansion theory was summarized,and the four building blo ks of the FMBEM-moment calculation,moment to moment translation,moment to local translation,and local to local translation,were described in detail.A data structure for the quad-tree construction was proposed which can facilitate the implementation.An analytical moment expression was derived which was more accurate,stable and efficient than direct numerical computation.Numerical examples were presented to demonstrate the accuracy and efficiency of the FMBEM,and the radiation of a 2D vibration rail mode was simulated using FMBEM.
- 2D acoustic wave problems,
- Helmholtz equation,
- fast multipole method,
- boundary element method

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References(30)

References

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