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.