Numerical analysis of the Landau-Lifshitz-Gilbert equation with inertial effects

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Ruggeri, Michele (2022) Numerical analysis of the Landau-Lifshitz-Gilbert equation with inertial effects. ESAIM: Mathematical Modelling and Numerical Analysis, 56 (4). pp. 1199-1222. ISSN 0764-583X (https://doi.org/10.1051/m2an/2022043)

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Abstract

We consider the numerical approximation of the inertial Landau-Lifshitz-Gilbert equation (iLLG), which describes the dynamics of the magnetisation in ferromagnetic materials at subpicosecond time scales. We propose and analyse two fully discrete numerical schemes: The first method is based on a reformulation of the problem as a linear constrained variational formulation for the linear velocity. The second method exploits a reformulation of the problem as a first order system in time for the magnetisation and the angular momentum. Both schemes are implicit, based on first-order finite elements, and generate approximations satisfying the unit-length constraint of iLLG at the vertices of the underlying mesh. For both methods, we prove convergence of the approximations towards a weak solution of the problem. Numerical experiments validate the theoretical results and show the applicability of the methods for the simulation of ultrafast magnetic processes.

ORCID iDs

Ruggeri, Michele ORCID logoORCID: https://orcid.org/0000-0001-6213-1602;
  • Item type:Article
    ID code:80625
    Dates:
    Date
    Event
    27 June 2022
    Published
    27 April 2022
    Published Online
    26 April 2022
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:10 May 2022 10:25
    Last modified:11 Nov 2024 13:28
    URI:https://strathprints.strath.ac.uk/id/eprint/80625
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