Effective simulation of a macroscopic model for stationary micromagnetics Original Research Article

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 without the exchange energy. The numerical simulation of the resulting minimization problem has to overcome difficulties caused by the pointwise side-restriction ∣m∣ ⩽ 1 and the stray field energy on the unbounded domain image. A penalty method models the side-restriction and the exterior Maxwell equation is recast via a nonlocal integral operator image. As shown in [Numer. Anal. Macrosc. Model Micromagnet, submitted for publication; Analysis, Numerik und Simulation eines Relaxierten Modellproblems zum Mikromagnetismus, doctoral thesis, Vienna University of Technology, 2003], the discretization leads to a nonlocal problem with piecewise constant ansatz and test functions and (dense) stiffness matrices with closed form formula for their entries. This paper addresses the numerical solution with Newton–Raphson schemes and the scientific computation of effective micromagnetic simulations.