Accelerated 3-D Numerical Scheme for the Evaluation of Hysteresis in Ferromagnetic Grains

The magnetic behavior of iron based ferromagnetic materials is important for the improvement of performances of electromagnetic devices. This paper deals with an accelerated 3-D model that computes the magnetic behavior of an iron grain under a varying applied field starting from its microscopic material parameters. The dynamics of the magnetic dipoles M in each space point of the grain is computed by integrating the Landau-Lifshitz equation using a semi-analytical predictor-corrector time stepping scheme. In the numerical computations, the spatial discretization is obtained by finite-different techniques. Evaluation of the magnetostatic field is done using fast Fourier transforms. This is the most time consuming part of the computations and in this paper we will demonstrate that this can be accelerated by computing the magnetostatic field on a higher discretization level. The values of the magnetostatic field in each finite-difference cell are determined through interpolation, still preserving an excellent precision.