Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics
Samuel Ferraz-Leite, Jens Markus Melenk, and Dirk Praetorius
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Submission date: 26. Aug. 2011
published in: Numerische Mathematik, 122 (2012) 1, p. 101-131
DOI number (of the published article): 10.1007/s00211-012-0454-z
MSC-Numbers: 65K05, 65K15, 49M20
Keywords and phrases: penalty method, quadratic programming, convex constraints, thin-film micromagnetics
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We analyze the reduced model for thin-film devices in stationary micromagnetics proposed by DeSimone, Kohn, Müller, Otto, Schäfer 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.