Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics
arXiv:1712.03795 · doi:10.1007/s10444-019-09667-z
Abstract
We consider the numerical approximation of the Landau-Lifshitz-Gilbert equation, which describes the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic contributions, the energy comprises the Dzyaloshinskii-Moriya interaction, which is the most important ingredient for the enucleation and the stabilization of chiral magnetic skyrmions. We propose and analyze three tangent plane integrators, for which we prove (unconditional) convergence of the finite element solutions towards a weak solution of the problem. The analysis is constructive and also establishes existence of weak solutions. Numerical experiments demonstrate the applicability of the methods for the simulation of practically relevant problem sizes.
References in corpus (6)
- Spontaneous Skyrmion Ground States in Magnetic Metals
- Asymmetric hysteresis for probing Dzyaloshinskii-Moriya interaction
- Domain structure of ultrathin ferromagnetic elements in the presence of Dzyaloshinskii-Moriya interaction
- Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation
- Convergence of an implicit-explicit midpoint scheme for computational micromagnetics
- Computational micromagnetics with Commics
Cited by in corpus (5)
- Three-Dimensional Chiral Magnetization Structures in FeGe Nanospheres
- Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics
- Computational micromagnetics with Commics
- Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics
- Local well-posedness for the Landau-Lifshitz equation with helicity term