Fast semianalytical time integration schemes for the Landau-Lifshitz equation

Aiming at a micromagnetic model that describes the macroscopic material behavior starting from microstructural features, there is a need for efficient time stepping schemes for the integration of Landau-Lifshitz-equation in material samples with dimensions of order [micro]m. This paper presents two related semianalytical time schemes. The time stepping algorithms are compared with other explicit time stepping schemes. Here, memory efficiency, time efficiency, convergence, and precision are checked. Further, special attention goes to 1) preservation of the magnetization magnitude in each FD cell; 2) a nonincrease of the free energy when applying a constant field; and 3) conservation of the systems free energy in the case of zero damping. Index Terms--Hysteresis, Landau-Lifshitz equation, micromagnetics, semianalytical integration.