Coarse-graining and Hierarchical Simulation of Magnetic Materials: the Fast Multipole Method

Abstract

The previous two chapters have discussed the micromagnetic simulation of magnetic materials. One of the most difficult problems in this area is dealing with the long range of the magnetic dipole interaction. Traditionally this problem is deal with by a mean field approach, assuming that the effect of distant dipoles is to produce a magnetic field locally that is proportional to the total magnetization of the system. There is a huge amount of literature on mean field approaches, but its accuracy is often such as to produce only qualitative rather than quantitatively correct results. Recently another approach has been developed to deal mathematically with the problem of long ranged interactions, known as the Fast Multipole Method (FMM). The original mathematical development of this method is rather complicated, but it has a simple physical interpretation for magnetic systems.