On stabilized models in micromagnetics

摘要

The effective behaviour of stationary micromagnetic phenomena is modelled by a convexified Landau–Lifshitz minimization problem for the limit of large and soft magnets Ω with no exchange energy. The numerical simulation of the resulting minimization problem has to overcome difficulties caused by the pointwise side-constraint $|bf{m}|leq 1$ and the stray-field energy on the unbounded domain $mathbb{R}^{d}$ . A penalty method models the side-constraint and the exterior Maxwell equation is recast via a nonlocal integral operator $mathcal{L}$ . This paper gives an overview of the available results and implementational details.