Adaptation and performance of the fast multipole method for dipolar systems

Abstract We have developed a new specialized version of the fast multipole method (FMM) for dipolar systems. For this purpose we have derived general expressions of the multipole expansion coefficients (in spherical coordinates) for a system of point dipoles with the potential ϕ dip ∼1/ r 2 . Our version is especially useful for simulations of fine magnetic particle systems (magnetic nanocomposites, ferrofluids), molecular dipolar fluids or electric dipolar glasses.