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P. Goldenits, D. Praetorius, D. Süss:
"Convergent geometric integrator for the Landau-Lifshitz-Gilbert equation in micromagnetics";
in: "ASC Report 19/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

We consider a lowest-order finite element scheme for the Landau-Lifshitz-Gilbert equation (LLG) which describes the dynamics
of micromagnetism. In contrast to previous works, we examine LLG with a total magnetic field which is induced by
several physical phenomena described in terms of exchange energy, anisotropy energy, magnetostatic energy, and Zeeman
energy. In our numerical scheme, the highest-order term which stems from the exchange energy, is treated implicitly, whereas
the remaining energy contributions are computed explicitly. Therefore, only one sparse linear system has to be solved per
time-step. The proposed scheme is unconditionally convergent to a global weak solution of LLG.

http://www.asc.tuwien.ac.at/preprint/2011/asc19x2011.pdf