[Back]

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