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

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