Fast multipole accelerated singular boundary method for the 3D Helmholtz equation in low frequency regime

This paper presents a fast multipole accelerated singular boundary method (SBM) to the solution of the large-scale three-dimensional Helmholtz equation at low frequency. By using a desingularization strategy to directly compute singular kernels in the strong-form collocation discretization, the SBM formulations are derived for the Dirichlet and Neumann problems. A fast multipole method (FMM) is then introduced to expedite the solution process. The CPU time and the memory requirement of the FMM-SBM scheme are both reduced to O(N), where N is the number of boundary nodes. Numerical examples with up to one million unknowns have been tested on a desktop computer. The results clearly illustrate that the proposed strategy appears very efficient and promising in solving large-scale Helmholtz problems.