The dynamics of the magnetization distribution in a ferromagnetic thin film problem is studied in this paper. The relaxation process of the magnetization distribution in a ferromagnetic material is described by the Landau-Lifshitz equation for the saturation magnetization \(M = M(t)\). On of the main difficulties in micromagnetic simulation is a severe time step constraint introduced by the exchange field. Using standard explicit integrators leads to a physical time step of sub-pico second, which is often two orders of magnitude smaller than the fastest physical time scales. Direct implicit integrators require solving complicated, coupled systems. In this paper the authors introduce an implicit method the complexity of which is comparable to solving the scalar heat equation implicitly. This method is based on a combination of a Gauss-Seidel implementation of a fractional step implicit solver for the gyromagnetic term, and the projection method for the heat flow of harmonic maps. This method allows to carry out fully resolved calculations for the switching of the magnetization in micron-sized elements.