A survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism

The Landau-Lifshitz (LL) equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also interesting mathematical properties of the LL equation: nonlocal character for some quantities, nonconvex side-constraints, strongly nonlinear terms. These effects influence also numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions, are addressed.