Simple recursive implementation of fast multipole method

In this paper we present an implementation of the well known “fast multipole” method (FMM) for the efficient calculation of dipole fields. The main advantage of the present implementation is simplicity—we believe that a major reason for the lack of use of FMMs is their complexity. One of the simplifications is the use of polynomials in the Cartesian coordinates rather than spherical harmonics. We have implemented it in the context of an arbitrary hierarchical system of cells—no periodic mesh is required, as it is for FFT (fast Fourier transform) methods. The implementation is in terms of recursive functions. Results are given for application to micromagnetic simulation. Complete source code is provided for an open-source implementation of this method, as well as an installer for the resulting program.