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Matem. Mod., 2014, Volume 26, Number 2, Pages 33–49 (Mi mm3447)  

This article is cited in 5 scientific papers (total in 5 papers)

Selection of an optimal numerical scheme for simulation system of the Landau–Lifshitz equations considering temperature fluctuations

E. Zipunovaa, A. Ivanovb

a Moscow Institute of Physics and Technology
b Keldysh Institute of Applied Mathematics (Russian Academy of Sciences)

Abstract: To create a variety of devices based on magnetic materials it is often necessary to conduct a large-scale simulation of different magnetic phenomena. The most appropriate is the so-called micromagnetic modeling based on a system of Landau–Lifshitz equations in which the evolution of the magnetic moments of individual particles is studied. Although this topic has been widely discussed, the question of taking into account the temperature fluctuations, which plays a key role in the description of phase transitions and the transition of the system from a state of unstable equilibrium during magnetization reversal, remains open. Accounting for temperature fluctuations imposes strong constraints on the intensity of the parasitic energy source generated by numerical scheme which in turn leads to substantial restrictions on the time step and reduce the count rate. In the paper two explicit numerical schemes have been proposed which are based on the analytic solution of the simplified problem of the evolution of magnetic moments of infinite sample with a body-centered cubic lattice in the spatially homogeneous case. New-constructed numerical schemes have been compared with classical Runge-Kutta methods for the initial conditions of the form of the Bloch domain wall, Neel domain wall and random initial conditions for a finite cylindrical sample. It is shown that one of the schemes is optimal in terms of maximizing the counting rate having fixed intensity of the source or drain of.

Keywords: Landau–Lifshitz equation, explicit methods, modeling magnetic materials.

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Received: 29.10.2012

Citation: E. Zipunova, A. Ivanov, “Selection of an optimal numerical scheme for simulation system of the Landau–Lifshitz equations considering temperature fluctuations”, Matem. Mod., 26:2 (2014), 33–49

Citation in format AMSBIB
\by E.~Zipunova, A.~Ivanov
\paper Selection of an optimal numerical scheme for simulation system of the Landau--Lifshitz equations considering temperature fluctuations
\jour Matem. Mod.
\yr 2014
\vol 26
\issue 2
\pages 33--49

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    This publication is cited in the following articles:
    1. S. A. Khilkov, A. V. Ivanov, E. V. Zipunova, “Numerical simulation of strongly nonequilibrium processes in magnetic materials based on the physical kinetics equations”, Math. Models Comput. Simul., 8:6 (2016), 703–708  mathnet  crossref  elib
    2. E. V. Zipunova, A. V. Ivanov, “K voprosu o testirovanii programmnykh kompleksov dlya modelirovaniya magnetikov”, Preprinty IPM im. M. V. Keldysha, 2017, 098, 30 pp.  mathnet  crossref
    3. A. V. Ivanov, “Raschet statisticheskoi summy i approksimatsiya mnogochastichnykh funktsii raspredeleniya dlya magnetikov v modeli Geizenberga”, Preprinty IPM im. M. V. Keldysha, 2019, 104, 12 pp.  mathnet  crossref
    4. A. V. Ivanov, “Approksimatsiya koeffitsientov uravneniya LandauLifshitsaBlokha pri mikromagnitnom modelirovanii”, Preprinty IPM im. M. V. Keldysha, 2019, 105, 16 pp.  mathnet  crossref
    5. A. V. Ivanov, “Uchet korrelyatsii mezhdu blizhaishimi sosedyami pri mikromagnitnom modelirovanii”, Preprinty IPM im. M. V. Keldysha, 2019, 118, 30 pp.  mathnet  crossref
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