Linear second-order IMEX-type integrator for the (eddy current) Landau–Lifshitz–Gilbert equation

Giovanni Di Fratta, Carl-Martin Pfeiler, Dirk Praetorius, Michele Ruggeri, Bernhard Stiftner

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
4 Downloads (Pure)

Abstract

Combining ideas from Alouges et al. (2014, A convergent and precise finite element scheme for Landau–Lifschitz–Gilbert equation. Numer. Math., 128, 407–430) and Praetorius et al. (2018, Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Comput. Math. Appl., 75, 1719–1738) we propose a numerical algorithm for the integration of the nonlinear and time-dependent Landau–Lifshitz–Gilbert (LLG) equation, which is unconditionally convergent, formally (almost) second-order in time, and requires the solution of only one linear system per time step. Only the exchange contribution is integrated implicitly in time, while the lower-order contributions like the computationally expensive stray field are treated explicitly in time. Then we extend the scheme to the coupled system of the LLG equation with the eddy current approximation of Maxwell equations. Unlike existing schemes for this system, the new integrator is unconditionally convergent, (almost) second-order in time, and requires the solution of only two linear systems per time step.

Original languageEnglish
Pages (from-to)2802-2838
Number of pages37
JournalIMA Journal of Numerical Analysis
Volume40
Issue number4
DOIs
Publication statusPublished - 31 Oct 2020

Keywords

  • finite elements
  • implicit-explicit time-marching scheme
  • linear second-order time integration
  • micromagnetism
  • unconditional convergence

Fingerprint

Dive into the research topics of 'Linear second-order IMEX-type integrator for the (eddy current) Landau–Lifshitz–Gilbert equation'. Together they form a unique fingerprint.

Cite this