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Advances in Computational Mathematics

, Volume 44, Issue 4, pp 1119–1151 | Cite as

Atomistic-continuum multiscale modelling of magnetisation dynamics at non-zero temperature

  • Doghonay ArjmandEmail author
  • Mikhail Poluektov
  • Gunilla Kreiss
Open Access
Article
  • 204 Downloads

Abstract

In this article, a few problems related to multiscale modelling of magnetic materials at finite temperatures and possible ways of solving these problems are discussed. The discussion is mainly centred around two established multiscale concepts: the partitioned domain and the upscaling-based methodologies. The major challenge for both multiscale methods is to capture the correct value of magnetisation length accurately, which is affected by a random temperature-dependent force. Moreover, general limitations of these multiscale techniques in application to spin systems are discussed.

Keywords

Multiscale modelling Micromagnetism Atomistic-continuum coupling Landau-Liftshitz-Gilbert equation 

Mathematics Subject Classification 2010

65C20 65M55 82C31 82D40 

Notes

Acknowledgements

The authors would like to acknowledge the support of eSSENCE. The authors would also like to acknowledge the support from the Swedish Research Council (VR) and the KAW foundation (grants 2013.0020 and 2012.0031).

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Doghonay Arjmand
    • 1
    • 2
    Email author
  • Mikhail Poluektov
    • 1
    • 3
  • Gunilla Kreiss
    • 1
  1. 1.Department of Information TechnologyUppsala UniversityUppsalaSweden
  2. 2.ANMC, Section de MathématiquesÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.International Institute for Nanocomposites Manufacturing, WMGUniversity of WarwickCoventryUK

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