L. Banas, M. Page, D. Praetorius:

"A general integrator for the Landau-Lifshitz-Gilbert equation";

in: "ASC Report 42/2012", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2012, ISBN: 978-3-902627-05-6, 1 - 4.

In our contribution, we extend a P1 finite element scheme for the

discretization of the Landau-Lifshitz-Gilbert equation (LLG), which

has originally been proposed by Alouges [1] for a simpler model

problem. Unlike prior works [2], [5], we allow arbitrary

contributions to the effective field and elaborate the circumstances

under which weak subconvergence towards a weak solution can

mathematically be guaranteed. Our analysis particularly includes

nonlinear, non-local, and/or time-dependent operators. In addition,

we investigate coupling of LLG to the full Maxwell´s equations and to

the conservation of momentum equation in order to include

magnetostrictive effects.

Landau-Lifshitz-Gilbert equation, multiscale problems, magnetostriction, Maxwell, finite elements, convergence analysis

http://www.asc.tuwien.ac.at/preprint/2012/asc42x2012.pdf

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