Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics

Gino Hrkac, Carl-Martin Pfeiler, Dirk Praetorius, Michele Ruggeri, Antonio Segatti, Bernhard Stiftner

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1329-1368
Number of pages40
JournalAdvances in Computational Mathematics
Issue number3
Early online date22 Apr 2019
Publication statusPublished - 1 Jun 2019


  • Dzyaloshinskii–Moriya interaction
  • finite element method
  • Landau–Lifshitz–Gilbert equation
  • magnetic skyrmions
  • micromagnetics


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