D. Praetorius, M. Ruggeri, B. Stiftner:

"Convergence of an implicit-explicit midpoint scheme for computational micromagnetics";

in: "ASC Report 23/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, ISBN: 978-3-902627-09-4, 1 - 27.

Based on lowest-order finite elements in space, we consider the numerical integration of the Landau-Lifschitz-Gilbert equation (LLG). The dynamics of LLG is driven by the so-called effective field which usually consists of the exchange field, the external field, and lower-order contributions such as the stray field. The latter equires the solution of an additional partial differential equation in full space. Following Bartels and Prohl (2006) [Convergence of an implicit finite element method for the Landau-Lifschitz-Gilbert equation.

SIAM J. Numer. Anal. 44(4):1405-1419], we combine the midpoint rule with an explicit Adams-Bashforth scheme. The resulting integrator is formally of second-order in time, and we prove unconditional convergence towards a weak solution of LLG. Numerical experiments underpin the theoretical findings.

http://www.asc.tuwien.ac.at/preprint/2016/asc23x2016.pdf

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