Mathematical and Numerical Studies of 1D Non Linear Ferromagnetic Materials

Patrick Joly 1 Olivier Vacus 1
1 ONDES - Modeling, analysis and simulation of wave propagation phenomena
Inria Paris-Rocquencourt, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR2706
Abstract : In this paper we are interested in the numerical modeling of absorbing ferromagnetic materials obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves. In this work we consider the 1D problem. We first show that the corresponding Cauchy problem has a unique global solution. We then derive a numerical scheme based on an appropriate modification of Yee's scheme, that we show to preserve some important properties of the continuous model such as the conservation of the norm of the magnetization and the decay of the electromagnetic energy. The stability is proved under a suitable CFL condition. Eventually some numerical results corresponding to the 1D model are presented.
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Patrick Joly, Olivier Vacus. Mathematical and Numerical Studies of 1D Non Linear Ferromagnetic Materials. [Research Report] RR-3024, INRIA. 1996. ⟨inria-00073669⟩

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