The mass-lumped midpoint scheme for computational micromagnetics : Newton linearization and application to magnetic skyrmion dynamics

Fratta, Giovanni Di and Pfeiler, Carl-Martin and Praetorius, Dirk and Ruggeri, Michele (2023) The mass-lumped midpoint scheme for computational micromagnetics : Newton linearization and application to magnetic skyrmion dynamics. Computational Methods in Applied Mathematics, 23 (1). pp. 145-175. ISSN 1609-9389 (https://doi.org/10.1515/cmam-2022-0060)

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Abstract

Abstract We discuss a mass-lumped midpoint scheme for the numerical approximation of the Landau–Lifshitz–Gilbert equation, which models the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic field contributions, our setting covers the non-standard Dzyaloshinskii–Moriya interaction, which is the essential ingredient for the enucleation and stabilization of magnetic skyrmions. Our analysis also includes the inexact solution of the arising nonlinear systems, for which we discuss both a constraint-preserving fixed-point solver from the literature and a novel approach based on the Newton method. We numerically compare the two linearization techniques and show that the Newton solver leads to a considerably lower number of nonlinear iterations. Moreover, in a numerical study on magnetic skyrmions, we demonstrate that, for magnetization dynamics that are very sensitive to energy perturbations, the midpoint scheme, due to its conservation properties, is superior to the dissipative tangent plane schemes from the literature.

ORCID iDs

Fratta, Giovanni Di, Pfeiler, Carl-Martin, Praetorius, Dirk and Ruggeri, Michele ORCID logoORCID: https://orcid.org/0000-0001-6213-1602;
  • Item type:Article
    ID code:80570
    Dates:
    Date
    Event
    1 January 2023
    Published
    9 June 2022
    Published Online
    22 March 2022
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:05 May 2022 13:41
    Last modified:11 Nov 2024 13:28
    URI:https://strathprints.strath.ac.uk/id/eprint/80570
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