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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
55/2011

Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics

Samuel Ferraz-Leite, Jens Markus Melenk and Dirk Praetorius

Abstract

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:
Aug 26, 2011
Published:
Aug 29, 2011
MSC Codes:
65K05, 65K15, 49M20
Keywords:
penalty method, quadratic programming, convex constraints, thin-film micromagnetics

Related publications

inJournal
2012 Journal Open Access
Samuel Ferraz-Leite, Jens Markus Melenk and Dirk Praetorius

Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics

In: Numerische Mathematik, 122 (2012) 1, pp. 101-131