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Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics
Samuel Ferraz-Leite, Jens Markus Melenk and Dirk PraetoriusAbstract
We analyze the reduced model for thin-film devices in stationary micromagnetics proposed by DeSimone, Kohn, M\"uller, Otto, Sch\"afer 2001. We introduce an appropriate functional analytic framework and prove well-posedness of the model in that setting. The scheme for the numerical approximation of solutions consists of two ingredients: The energy space is discretized in a conforming way using Raviart-Thomas finite elements; the non-linear but convex side constraint is treated with a penalty method. This strategy yields a convergent sequence of approximations as discretization and penalty parameter vanish. The proof generalizes to a large class of minimization problems and is of interest beyond the scope of thin-film micromagnetics. Numerical experiments support our findings and illustrate the performance of the proposed algorithm.
- Received:
- 26.08.11
- Published:
- 29.08.11
- MSC Codes:
- 65K05, 65K15, 49M20
- Keywords:
- penalty method, quadratic programming, convex constraints, thin-film micromagnetics