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hille-yosida theorem

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Mathematical and numerical studies ofnon linear ferromagnetic materials
Patrick Joly, Olivier Vacus
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 33 / Issue 3 / May 1999

Published online by Cambridge University Press:

15 August 2002, pp. 593-626

Print publication:

May 1999
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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.

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Mathematical and numerical studies ofnon linear ferromagnetic materials

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Mathematical and numerical studies ofnon linear ferromagnetic materials