Using multipoles decreases computation time for magnetostatic self-energy

The calculation of the magnetostatic self-energy and field is the most computationally intensive aspect of micromagnetics simulations. The computation time is proportional to N², where N is the number of cells in the discretized problem. The authors have implemented an algorithm that uses multipole expansions of the field integrals for cells suitably far from the field evaluation point. The computation time is asymptotically proportional to N log N. This implementation is demonstrated by computing the micromagnetic structure of domain walls in both thin and thick ferromagnetic films