Functional Analytic Framework for a Reduced Model in Thin-film Micromagnetics
نویسنده
چکیده
The steady state of a magnetization M of a ferromagnetic sample Ω 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. For uniaxial material with easy axis e1, the free micromagnetic energy reads E(M) = d ∫
منابع مشابه
Reduced Model in Thin-film Micromagnetics
The full minimization problem in micromagnetics due to Landau and Lifschitz is, from a numerical point of view, very complex. In [7] a reduced model in thin-film micromagnetics has been proposed and analyzed with focus on a distributional point of view. In contrast, we present a functional analytic framework which is more suitable for numerical analysis. Well-posedness of the model problem in t...
متن کاملNumerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics
We analyze the reduced model for thin-film devices in stationary micromagnetics proposed in [7, 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 ...
متن کاملNumerical Methods for a Reduced Model in Thin{Film Micromagnetics
Diese Arbeit ist meiner Familie gewidmet. The great sense of passing through.
متن کاملOptimal grid-based methods for thin film micromagnetics simulations
Thin filmmicromagnetics are a broad class ofmaterials withmany technological applications, primarily inmagneticmemory. The dynamics of the magnetization distribution in these materials is traditionally modeled by the Landau–Lifshitz– Gilbert (LLG) equation. Numerical simulations of the LLG equation are complicated by the need to compute the stray field due to the inhomogeneities in the magnetiz...
متن کاملFinite Element Discretization of a Reduced Model in Thin-film Micromagnetics
We consider the reduced model proposed in [3] which is consistent with the prior works [1] and [4] and is valid for sufficiently large and thin ferromagnetic samples. Let ω ⊆ R denote a bounded Lipschitz domain with diameter l = 1. This domain represents our ferromagnetic sample Ω = ω × [0, t], whose thickness t > 0 is neglected for simplicity. Here, we consider a uniaxial material with in-plan...
متن کامل