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Title: Beyond first-order finite element schemes in micromagnetics

Abstract

Magnetization dynamics in ferromagnetic materials is ruled by the Landau–Lifshitz–Gilbert equation (LLG). Reliable schemes must conserve the magnetization norm, which is a nonconvex constraint, and be energy-decreasing unless there is pumping. Some of the authors previously devised a convergent finite element scheme that, by choice of an appropriate test space – the tangent plane to the magnetization – reduces to a linear problem at each time step. The scheme was however first-order in time. We claim it is not an intrinsic limitation, and the same approach can lead to efficient micromagnetic simulation. We show how the scheme order can be increased, and the nonlocal (magnetostatic) interactions be tackled in logarithmic time, by the fast multipole method or the non-uniform fast Fourier transform. Our implementation is called feeLLGood. A test-case of the National Institute of Standards and Technology is presented, then another one relevant to spin-transfer effects (the spin-torque oscillator)

Authors:
 [1]; ;  [2];  [3];  [4]
  1. Laboratoire d'analyse, géométrie et applications, université Paris 13, CNRS UMR 7539, 93430 Villetaneuse (France)
  2. SPINTEC, INAC, UMR CEA/CNRS/UJF-Grenoble 1/Grenoble-INP, F-38054 Grenoble (France)
  3. CMAP, CNRS and École polytechnique, F-91128 Palaiseau (France)
  4. Institut Néel, CNRS and université Joseph Fourier, F-38042 Grenoble (France)
Publication Date:
OSTI Identifier:
22230837
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 256; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS; FERROMAGNETIC MATERIALS; FINITE ELEMENT METHOD; FOURIER TRANSFORMATION; IMPLEMENTATION; INTERACTIONS; LIMITING VALUES; MAGNETIZATION; OSCILLATORS; SIMULATION; SPACE; SPIN; TORQUE

Citation Formats

Kritsikis, E., E-mail: kritsikis@math.univ-paris13.fr, Vaysset, A., Buda-Prejbeanu, L.D., Alouges, F., and Toussaint, J.-C. Beyond first-order finite element schemes in micromagnetics. United States: N. p., 2014. Web. doi:10.1016/J.JCP.2013.08.035.
Kritsikis, E., E-mail: kritsikis@math.univ-paris13.fr, Vaysset, A., Buda-Prejbeanu, L.D., Alouges, F., & Toussaint, J.-C. Beyond first-order finite element schemes in micromagnetics. United States. doi:10.1016/J.JCP.2013.08.035.
Kritsikis, E., E-mail: kritsikis@math.univ-paris13.fr, Vaysset, A., Buda-Prejbeanu, L.D., Alouges, F., and Toussaint, J.-C. 2014. "Beyond first-order finite element schemes in micromagnetics". United States. doi:10.1016/J.JCP.2013.08.035.
@article{osti_22230837,
title = {Beyond first-order finite element schemes in micromagnetics},
author = {Kritsikis, E., E-mail: kritsikis@math.univ-paris13.fr and Vaysset, A. and Buda-Prejbeanu, L.D. and Alouges, F. and Toussaint, J.-C.},
abstractNote = {Magnetization dynamics in ferromagnetic materials is ruled by the Landau–Lifshitz–Gilbert equation (LLG). Reliable schemes must conserve the magnetization norm, which is a nonconvex constraint, and be energy-decreasing unless there is pumping. Some of the authors previously devised a convergent finite element scheme that, by choice of an appropriate test space – the tangent plane to the magnetization – reduces to a linear problem at each time step. The scheme was however first-order in time. We claim it is not an intrinsic limitation, and the same approach can lead to efficient micromagnetic simulation. We show how the scheme order can be increased, and the nonlocal (magnetostatic) interactions be tackled in logarithmic time, by the fast multipole method or the non-uniform fast Fourier transform. Our implementation is called feeLLGood. A test-case of the National Institute of Standards and Technology is presented, then another one relevant to spin-transfer effects (the spin-torque oscillator)},
doi = {10.1016/J.JCP.2013.08.035},
journal = {Journal of Computational Physics},
number = ,
volume = 256,
place = {United States},
year = 2014,
month = 1
}
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