The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Improvements both on a numerical and computational basis can relief problems related to this bottleneck. This work presents an efficient implementation of the Fast Multipole Method [FMM] for the magnetic scalar potential as used in micromagnetics. We assume linearly magnetized tetrahedral sources, treat the near field directly and use analytical integration on the multipole expansion in the far field. This approach tackles important issues like the vectorial and continuous nature of the magnetic field. By using FMM the calculations scale linearly in time and memory.

The Stoner-Wohlfarth model provides an efficient analytical model to describe the behavior of magnetic layers within xMR sensors. Combined with a proper description of magneto-resistivity an efficient device model can be derived, which is necessary for an optimal electric circuit design. Parameters of the model are determined by global optimization of an application specific cost function which contains measured resistances for different applied fields. Several application cases are examined and used for validation of the device model. Furthermore the applicability of the SW model is verified by comparison with micromagnetic energy minimization results.

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Fast stray field calculation is commonly considered of great importance for micromagnetic simulations, since it is the most time consuming part of the simulation. The Fast Multipole Method (FMM) has displayed linear O(N) parallelization behavior on many cores. This article investigates the error of a recent FMM approach approximating sources using linear—instead of constant—finite elements in the singular integral for calculating the stray field and the corresponding potential. After measuring performance in an earlier manuscript, this manuscript investigates the convergence of the relative L2 error for several FMM simulation parameters. Various scenarios either calculating the stray field directly or via potential are discussed.