We present a steepest descent energy minimization scheme for micromagnetics. The method searches on a curve that lies on the sphere which keeps the magnitude of the magnetization vector constant. The step size is selected according to a modified Barzilai-Borwein method. Standard linear tetrahedral finite elements are used for space discretization. For the computation of static hysteresis loops the steepest descent minimizer is faster than a Landau-Lifshitz micromagnetic solver by more than a factor of two. The speed up on a graphic processor is 4.8 as compared to the fastest single-core CPU implementation.

A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N4/3 for N computational cells used and with N2/3 (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples.

The coercive field of permanent magnets decays with temperature. At non-zero temperature the system can overcome a finite energy barrier through thermal fluctuations. Using finite element micromagnetic simulations, we quantify this effect, which reduces coercivity in addition to the decrease of the coercive field associated with the temperature dependence of the anisotropy field, and validate the method through comparison with existing experimental data.

Exchange coupled ferri-/ferromagnetic heterostructures are a possible material composition for future magnetic storage and sensor applications. In order to understand the driving mechanisms in the demagnetization process, we perform micromagnetic simulations by employing the Landau–Lifshitz–Gilbert equation. The magnetization reversal is dominated by pinning events within the amorphous ferrimagnetic layer and at the interface between the ferrimagnetic and the ferromagnetic layer. The shape of the computed magnetization reversal loop corresponds well with experimental data, if a spatial variation of the exchange coupling across the ferri-/ferromagnetic interface is assumed.

In the field of biomedicine magnetic beads are used for drug delivery and to treat hyperthermia. Here we propose to use self-organized bead structures to isolate circulating tumor cells using lab-on-chip technologies. Typically blood flows past microposts functionalized with antibodies for circulating tumor cells. Creating these microposts with interacting magnetic beads makes it possible to tune the geometry in size, position and shape. We developed a simulation tool that combines micromagnetics and discrete particle dynamics, in order to design micropost arrays made of interacting beads. The simulation takes into account the viscous drag of the blood flow, magnetostatic interactions between the magnetic beads and gradient forces from external aligned magnets. We developed a particle-particle particle-mesh method for effective computation of the magnetic force and torque acting on the particles.