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Issue ESAIM: Proc.
Volume 22, 2008
CANUM 2006 - Congrès National d'Analyse Numérique
Page(s) 114 - 117
DOI http://dx.doi.org/10.1051/proc:072212
Published online 01 February 2008

ESAIM: Proc., 2008, Vol. 22, pp. 114-117
DOI: 10.1051/proc:072212

Mathematical models in micromagnetism: an introduction

Francois Alouges

Laboratoire de Mathématiques, Bât. 425, Université Paris 11, 91405 Orsay Cedex, France


(Published online: 1 February 2008)

Abstract
The modelization of ferromagnetic materials obeys the micromagnetic theory proposed by W. F. Brown [4] for static configurations and the Landau-Lifchitz (or Landau-Lifchitz-Gilbert) equations for the dynamics. In this paper, we briefly present these underlying models. Difficulties including physical relevance, numerical simulations and analytic properties of the equations that one wants to keep at the discrete level are discussed.


Résumé
La modélisation de matériaux ferromagnétiques suit la théorie du micromagnétisme proposée par Brown pour les configurations statiques (d'équilibre) et les équations de Landau-Lifchitz (ou Landau-Lifchitz-Gilbert) pour la dynamique. Dans ce papier, nous décrivons rapidement les principaux modèles utilisés. Les difficultés incluant la pertinence physique, les simulations numériques ainsi que le respect au niveau discret des propriétés analytiques du modèle sont précisées.


Mathematics Subject Classification. 35Q60, 65Z05

Key words: Micromagnetism, Landau-Lifchitz equations


© EDP Sciences, ESAIM 2007


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