8.2 Finite element model

The program package implementing the micromagnetic finite element model has already been developed and used for deterministic simulations [8]. The time integration was performed by an implicit backward difference or alternatively by a Runge-Kutta time integration scheme. Thus, it was only necessary to replace the deterministic time integration algorithm by the stochastic Heun scheme ().

The main advantages of the finite element model are, that it calculates the magnetostatic field using a magnetic scalar potential and reduces the computational effort of treating the open boundary problem by a hybrid finite element/boundary element method [37]. Furthermore, it is easy to simulate arbitrary geometries with curved surfaces, which cause many problems in finite difference simulations.