中文摘要：

快速多极子边界元算法可以加速矩阵和向量乘法运算,将传统边界元算法的计算量和内存占用量分别降为O（Nlog~2N）和O（N）,适用于大型声学模型模拟计算.本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法.将新的自适应树状算法应用到对角形式的快速多极子边界元算法,并使用最新提出的解析式源点矩计算公式,进一步提高了快速多极子边界元的计算效率.绝对软球体在内部共振频率处的散射声场计算,验证了所发展算法在共振频率处求解的正确性.与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较,验证了算法及程序在大型模型声学计算中的准确性,同时显示了其求解的高效性.最后,将该算法用于车内声场及水下声学探测的分析计算.

英文摘要：

It is suitable to solve the acoustic problems by using the fast multipole boundary element method （FMBEM）, since the FMBEM can accelerate the matrix-vector multiplication dramatically by reducing the CPU time and memory of conventional boundary element method to O（Nlog2N） and O（N） respectively. We propose a 3D acoustic FMBEM based on Burton-Miller formulation in this paper. A new adaptive algorithm is applied to the diagonal form FMBEM, and a new proposed analytical moment formulation is used in the moment computation. Both of them further improve the efficiency of FMBEM. Acoustic scattering of soft sphere at resonant frequency is investigated to validate the accuracy of solution using Burton-Miller formulation. Comparisons of solution to the multi-radiating spheres problem with the one solved by Bapat＇s program demonstrate the accuracy and the efficiency of our algorithm in solving large-scale acoustic problems. In the end, we use our algorithm to analyze the inner sound filed of a car and dolphin acoustic scattering.