Linear second-order IMEX-type integrator for the (eddy current) Landau–Lifshitz–Gilbert equation
Di Fratta, Giovanni and Pfeiler, Carl-Martin and Praetorius, Dirk and Ruggeri, Michele and Stiftner, Bernhard (2020) Linear second-order IMEX-type integrator for the (eddy current) Landau–Lifshitz–Gilbert equation. IMA Journal of Numerical Analysis, 40 (4). pp. 2802-2838. ISSN 0272-4979 (https://doi.org/10.1093/imanum/drz046)
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Abstract
Combining ideas from Alouges et al. (2014, A convergent and precise finite element scheme for Landau–Lifschitz–Gilbert equation. Numer. Math., 128, 407–430) and Praetorius et al. (2018, Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Comput. Math. Appl., 75, 1719–1738) we propose a numerical algorithm for the integration of the nonlinear and time-dependent Landau–Lifshitz–Gilbert (LLG) equation, which is unconditionally convergent, formally (almost) second-order in time, and requires the solution of only one linear system per time step. Only the exchange contribution is integrated implicitly in time, while the lower-order contributions like the computationally expensive stray field are treated explicitly in time. Then we extend the scheme to the coupled system of the LLG equation with the eddy current approximation of Maxwell equations. Unlike existing schemes for this system, the new integrator is unconditionally convergent, (almost) second-order in time, and requires the solution of only two linear systems per time step.
ORCID iDs
Di Fratta, Giovanni, Pfeiler, Carl-Martin, Praetorius, Dirk, Ruggeri, Michele ORCID: https://orcid.org/0000-0001-6213-1602 and Stiftner, Bernhard;-
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Item type: Article ID code: 80632 Dates: DateEvent31 October 2020Published27 February 2019AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 10 May 2022 13:38 Last modified: 11 Nov 2024 13:28 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/80632