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Mathematical and numerical studies ofnon linear ferromagnetic materials

Published online by Cambridge University Press:  15 August 2002

Patrick Joly  and
Olivier Vacus
Patrick Joly
Affiliation:
INRIA Rocquencourt, 78153 Le Chesnay Cedex, France. Patrick.Joly@inria.fr.
Olivier Vacus
Affiliation:
Dassault Aviation, 92214 Saint-Cloud Cedex, France. olivier.vacus@dassault-aviation.fr.
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Abstract

In this paper we are interested in the numerical modelingof absorbing ferromagnetic materialsobeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves.In this workwe consider the 1D problem. We first show that the corresponding Cauchy problemhas a unique global solution. We then derive a numerical scheme based on an appropriate modificationof Yee's scheme, that we show to preserve some importantproperties of the continuous model such as the conservation of the normof the magnetization and the decay of the electromagnetic energy.Stability is proved under a suitable CFL condition.Some numerical results for the 1D model are presented.

Keywords

Maxwell equationsLaundau-Lifchitz-Gilbert equationHille-Yosida theoremFDTD.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 3 , May 1999 , pp. 593 - 626
Copyright
© EDP Sciences, SMAI, 1999

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