Application of the fast multipole method for the evaluation of magnetostatic fields in micromagnetic computations

Micromagnetic simulations are elaborated to describe the magnetic dynamics in ferromagnetic bodies. In these simulations, most of the time is spent on the evaluation of the magnetostatic field in the magnetic material. This paper presents a new numerical finite difference scheme for the evaluation of the magnetostatic field based on the fast multipole method (FMM). The interactions between finite difference cells are described in terms of far and near field interactions. The far field computations are conducted using the spherical harmonic expansion of the magnetostatic field while the near field computations are accelerated using fast Fourier transforms (FFT). The performance of the presented FMM scheme is studied by comparing the scheme with a pure FFT scheme. The FMM scheme is more memory efficient and more flexible then the FFT scheme. It is accurate and still has a good time efficiency.