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

作　　者：吴海军 蒋伟康 Y．J．LIU 

机构地区：[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　　处：《Applied Mathematics and Mechanics(English Edition)》2011年第8期981-996,共16页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.11074170);the State Key Laboratory Foundation of Shanghai Jiao Tong University(No.MSVMS201105)

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.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.

关 键 词：2D acoustic wave problem Helmholtz equation fast multipole method boundary element method 

分 类 号：O42[理学—声学] O241.82[理学—物理]