  An implementation of the fast multiple method (FMM) is performed for magnetic
systems with long-ranged dipolar interactions. Expansion in spherical harmonics
of the original FMM is replaced by expansion of polynomials in Cartesian
coordinates, which is considerably simpler. Under open boundary conditions, an
expression for multipole moments of point dipoles in a cell is derived. These
make the program appropriate for nanomagnetic simulations, including magnetic
nanoparticles and ferrofluids. The performance is optimized in terms of cell
size and parameter set (expansion order and opening angle) and the trade off
between computing time and accuracy is quantitatively studied. A rule of thumb
is proposed to decide the appropriate average number of dipoles in the smallest
cells, and an optimal choice of parameter set is suggested. Finally, the
superiority of Cartesian coordinate FMM is demonstrated by comparison to
spherical harmonics FMM and FFT.
