Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics
This work provides rigorous numerical analysis for a key equation in micromagnetics, enabling reliable simulation of skyrmion dynamics for researchers in computational physics and materials science.
The paper proposes and analyzes three convergent tangent plane integrators for the Landau-Lifshitz-Gilbert equation with Dzyaloshinskii-Moriya interaction, proving unconditional convergence of finite element solutions to weak solutions and demonstrating applicability for simulating chiral magnetic skyrmion dynamics.
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.