二维声场预测的快速多极基本解法

传统基本解法在二维大规模模型的声场求解过程中,系统方程形成和求解的计算量正比于自由度N的二次方O(N2)和三次方O(N3),求解效率低;为此,引入快速多极子算法并采用广义极小残差法迭代求解,提出一种用于二维声场预测的快速多极基本解法。对无限长圆柱体及二维类车体辐射模型的仿真结果表明,当N为3000时,分别采用快速多极基本解法与传统基本解法求解所需的时间比值约为百分之四,且N越大比值越小;最终实现系统方程的形成和求解的计算量降低到正比于自由度O(N),提高了对二维大规模模型声场预测计算效率。 

A fast multipole method of fundamental solutions for two dimensional acoustic radiation problems

The method of fundamental solutions (MFS) for two dimensional (2D) large scale acoustic problems requires O(N^2) operations in formulations and O(N3) in a direct solution of the linear system, where N is the number of unknowns, and it also needs large memory storage and has low computational efficiency. A fast multipole method of fundamental solutions (FMMFS) for two dimensional acoustic radiation problems is presented, by combining the method of fundamental solutions (MFS) with the fast multipole method (FMM), and an iterative equation solver called the Generalized Minimum Residual method (GMRES) is used in the FMMFS. The numerical examples of a long pulsating cylinder and 2D car-like model radiation problems are presented, and they clearly demonstrate that the ratio of solution time using the FMMFS and MFS respectively is approximately four percent, when the N is equal to 3000, and the larger N the smaller ratio. Compared with the traditional MFS, the operations in formulations and solution of the linear system with the developed FMMFS are both reduced to O(N), and the efficiency for 2D large scale acoustic problems is greatly improved.