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

Abstract

We analyze the reduced model for thin-film devices in stationary micromagnetics proposed in DeSimone et al. (R Soc Lond Proc Ser A Math Phys Eng Sci 457(2016):2983-2991). 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.Mathematics Subject Classification (2010) 65K05 · 65K15 · 49M20 1 Introduction and abstract setting

FEM–BEM coupling for the large-body limit in micromagnetics

“…From this, we deduce Combining (3.14) and (3.15) implies : For sufficiently smooth magnetizations, this follows by classical calculus. In the present setting of distributions, smoothing arguments have to be employed as shown in [20, Satz 2.12] or [21, Lemma 14] . This concludes the proof.…”