Fast multipole method for micromagnetic simulation of periodic systems

We have developed a new method for computing the magnetostatic field of an infinite array of images of an arbitrary system of charges or multipoles. The result takes the form of a Taylor expansion of the potential of a "cored array" of distant images, as is required by the fast multipole method, the most efficient method known for calculating magnetostatic fields in very large systems. The new method is much faster and simpler to implement than the usual Ewald summation or fast Fourier transform, and does not require a regular grid inside the central cell.