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S. Ferraz-Leite, J. Melenk, D. Praetorius:
"Energy minimization in thin-film micromagnetics";
Talk: 17th ÖMG Congress / Annual DMV Conference, Graz; 2009-09-21 - 2009-09-25.

The steady state of a magnetization M of a ferromagnetic sample W was first described by Landau and Lifschitz as the solution of a certain minimization problem, which is nowadays accepted as the relevant model to describe micromagnetic phenomena. However, micromagnetics is one prototype of a non-convex and nonlocal multiscale problem and, from a numerical point of view, thus hardly accessible. In [DeSimone, Kohn, Müller, Otto and Schäfer, 2001], a reduced model for thin-film micromagnetics has been introduced which is consistent with the prior works [Bryant and Suhl, 1989] and [van den Berg, 1986]. Let ω in R² denote a bounded Lipschitz domain with diameter l = 1. This domain represents our ferromagnetic sample Ω = ω x [0, t], whose thickness t > 0 is neglected for simplicity. Here, we consider a uniaxial material with in-plane easy axis e1. With an applied exterior field f : ω -> R², we seek a minimizer m of the reduced thin-film energy as proposed by [DeSimone, Kohn, Müller, Otto, and Schäfer 2001].

In contrast to [DeSimone, Kohn, Müller, and Otto, 2002] and [Drwenski, 2008], where the focus is on a distributional point of
view, we give a precise and appropriate functional analytic framework in a certain subspace of H^1/2(div,ω). Existence
and uniqueness of a minimizer m in our functional setting is proven. We propose a numerical discretization strategy by use of lowest-order Raviart-Thomas finite elements and provide a priori error estimates. First numerical examples conclude the talk.

Thin-film micromagnetics, micromagnetics, Raviart-Thomas, constraint minimization

http://publik.tuwien.ac.at/files/PubDat_177780.pdf