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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (8): 981-996.doi: https://doi.org/10.1007/s10483-011-1474-7

• Articles • 上一篇    下一篇

Diagonal form fast multipole boundary element method for 2D acoustic problems based on Burton-Miller boundary integral equation formulation and its applications

吴海军1 蒋伟康1 Liu, Y. J.2   

  1. 1. State Key Laboratory of Machinery System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;
    2. Mechanical Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0072, USA
  • 出版日期:2011-08-20 发布日期:2011-08-20

Diagonal form fast multipole boundary element method for 2D acoustic problems based on Burton-Miller boundary integral equation formulation and its applications

 WU Hai-Jun1, JIANG Wei-Kang1, Liu, Y. J.2   

  1. 1. State Key Laboratory of Machinery System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;
    2. Mechanical Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0072, USA
  • Online:2011-08-20 Published:2011-08-20

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摘要： This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.

Abstract: This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.

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