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

@article{Cimrk2007ASO,
  title={A Survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism},
  author={Ivan Cimr{\'a}k},
  journal={Archives of Computational Methods in Engineering},
  year={2007},
  volume={15},
  pages={1-37}
}
  • I. Cimrák
  • Published 2007
  • Mathematics
  • Archives of Computational Methods in Engineering
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 an interesting mathematical properties of the LL equation: nonlocal character for some quantities,nonconvex side-constraints, strongly nonlinear terms. These effects influence also the numerical approximations. In this work, recent developments on… 
3 Citations

A reduced model for domain wall dynamics in soft ferromagnets

Micromagnetics and spintronics: models and numerical methods

  • C. Abert
  • Engineering
    The European Physical Journal B
  • 2019
An overview over the analytical micromagnetic model as well as its numerical implementation is given on the integration of spin-transport effects with classical micromagnetics.

A convergent evolving finite element algorithm for mean curvature flow of closed surfaces

The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the discrete surface like in Dziuk's method, and linearly implicit backward difference formulae for time integration and discretizes Huisken's evolution equations for the normal vector and mean curvature.