An Implementation of the Fast Multipole Method without Multipoles

An implementation is presented of the fast multipole method, which uses approximations based on Poisson’s formula. Details for the implementation in both two and three dimensions are given. Also discussed is how the multigrid aspect of the fast multipole method can be exploited to yield efficient programming procedures. The issue of the selection of an appropriate refinement level for the method is addressed. Computational results are given that show the importance of good level selection. An efficient technique that can be used to determine an optimal level to choose for the method is presented.