Second-order semi-implicit projection methods for micromagnetics simulations

Changjian Xie, Carlos J. García-Cervera, Cheng Wang, Zhennan Zhou, Jingrun Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

Micromagnetics simulations require accurate approximation of the magnetization dynamics described by the Landau-Lifshitz-Gilbert equation, which is nonlinear, nonlocal, and has a non-convex constraint, posing interesting challenges in developing numerical methods. In this paper, we propose two second-order semi-implicit projection methods based on the second-order backward differentiation formula and the second-order interpolation formula using the information at previous two temporal steps. Unconditional unique solvability of both methods is proved, with their second-order accuracy verified through numerical examples in both 1D and 3D. The efficiency of both methods is compared to that of another two popular methods. In addition, we test the robustness of both methods for the first benchmark problem with a ferromagnetic thin film material from National Institute of Standards and Technology.

Original languageEnglish
Article number109104
JournalJournal of Computational Physics
Volume404
DOIs
Publication statusPublished - 1 Mar 2020
Externally publishedYes

Keywords

  • Backward differentiation formula
  • Hysteresis loop
  • Landau-Lifshitz-Gilbert equation
  • Micromagnetics simulation
  • Second-order accuracy

Fingerprint

Dive into the research topics of 'Second-order semi-implicit projection methods for micromagnetics simulations'. Together they form a unique fingerprint.

Cite this