Convergence of an implicit–explicit midpoint scheme for computational micromagnetics

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Praetorius, Dirk and Ruggeri, Michele and Stiftner, Bernhard (2018) Convergence of an implicit–explicit midpoint scheme for computational micromagnetics. Computers and Mathematics with Applications, 75 (5). pp. 1719-1738. ISSN 0898-1221 (https://doi.org/10.1016/j.camwa.2017.11.028)

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Abstract

Based on lowest-order finite elements in space, we consider the numerical integration of the Landau–Lifschitz–Gilbert equation (LLG). The dynamics of LLG is driven by the so-called effective field which usually consists of the exchange field, the external field, and lower-order contributions such as the stray field. The latter requires the solution of an additional partial differential equation in full space. Following Bartels and Prohl (2006), we employ the implicit midpoint rule to treat the exchange field. However, in order to treat the lower-order terms effectively, we combine the midpoint rule with an explicit Adams–Bashforth scheme. The resulting integrator is formally of second-order in time, and we prove unconditional convergence towards a weak solution of LLG. Numerical experiments underpin the theoretical findings.

ORCID iDs

Praetorius, Dirk, Ruggeri, Michele ORCID logoORCID: https://orcid.org/0000-0001-6213-1602 and Stiftner, Bernhard;
  • Item type:Article
    ID code:80559
    Dates:
    Date
    Event
    1 March 2018
    Published
    26 November 2017
    Accepted
    Notes:Funding Information: The authors acknowledge support of the Vienna Science and Technology fund (WWTF) under grant MA14-44 , of the Austrian Science Fund (FWF) under grant W1245 , and of TU Wien through the innovative projects initiative. We thank Alexander Rieder (TU Wien) and Alexander Haberl (TU Wien) for their help with coupling NGSolve to the BEM++ library. Publisher Copyright: © 2017 Elsevier Ltd
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:05 May 2022 09:38
    Last modified:11 Nov 2024 13:28
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/80559
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