Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics

Kraus, Johannes and Pfeiler, Carl Martin and Praetorius, Dirk and Ruggeri, Michele and Stiftner, Bernhard (2019) Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics. Journal of Computational Physics, 398. 108866. ISSN 0021-9991 (https://doi.org/10.1016/j.jcp.2019.108866)

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Abstract

The tangent plane scheme is a time-marching scheme for the numerical solution of the nonlinear parabolic Landau–Lifshitz–Gilbert equation, which describes the time evolution of ferromagnetic configurations. Exploiting the geometric structure of the equation, the tangent plane scheme requires only the solution of one linear variational form per time-step, which is posed in the discrete tangent space determined by the nodal values of the current magnetization. We develop an effective solution strategy for the arising constrained linear systems, which is based on appropriate Householder reflections. We derive possible preconditioners, which are (essentially) independent of the time-step, and prove linear convergence of the preconditioned GMRES algorithm. Numerical experiments underpin the theoretical findings.

ORCID iDs

Kraus, Johannes, Pfeiler, Carl Martin, Praetorius, Dirk, Ruggeri, Michele ORCID logoORCID: https://orcid.org/0000-0001-6213-1602 and Stiftner, Bernhard;
  • Item type:Article
    ID code:80553
    Dates:
    Date
    Event
    1 December 2019
    Published
    6 August 2019
    Published Online
    30 July 2019
    Accepted
    Notes:Funding Information: Acknowledgments. The authors acknowledge support from the Vienna Science and Technology Fund (WWTF) through grant MA14-44 and the Austrian Science Fund (FWF) through grants DK W1245 and SFB F65. Publisher Copyright: © 2019 Elsevier Inc.
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:05 May 2022 08:00
    Last modified:11 Nov 2024 13:28
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/80553
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