基于Burton-Miller边界积分方程的二维声学波动问题对角形式快速多极子边界元及其应用

论述了二维声学问题的快速多极子边界元（FMBEM）方程及实现步骤．概述了核函数展开理论，并对FMBEM的4个重要组成部分:源点矩计算、源点矩转移、源点矩至本地展开转移、本地展开转移进行了详细的描述．提出了一种有利于四叉树建立的数据结构．推导了一种比直接数值计算更精确、稳定和高效的解析源点矩计算公式．数值算例验证了FMBEM的正确性和高效性．最后，使用FMBEM对轨道二维声学辐射模型进行了模拟计算．

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

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.