Many research groups use the finite difference method for their micromagnetic simulations. The calculation of the demagnetizing field is often done by more advanced methods based on the analytic solution for homogeneously magnetized hexahedra [23] or fast Fourier transformations [28,29]. However, stiff modes cause deteriorating convergence rates [30].
Another problem arises from complicated geometries (possibly with curved boundaries) and irregular microstructures. As the finite difference method requires the use of a regular lattice, it is difficult to handle curved boundaries, because they are always approximated by small steps. Only recently, the ``Embedded Curved Boundary Method'' succeeded in generating results similar to those of the finite element method [31,32].