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Inversion de systèmes linéaires pour la simulation des matériaux ferromagnétiques. Singularités d'une configuration d'aimantation

Abstract : In this thesis, we study two mathematical problems concerning the equations of micromagnetism. These equations govern the configuration of the magnetization in the ferromagnetic materials which enter the fabrication of magnetic heads and Bloch lines memories. In the first part, we describe the physical properties of these materials and give a brief description of the two numerical codes, that have been developed at the LETI-CEA. A configuration of magnetization is a minimum of an energy composed of four terms : the energies of exchange, anisotropy, demagnetization and of Zeemann. Furthermore, the magnetization has a constant norm. It is a problem of minimization of a non quadratique functional, under a non linear constraint. The demagnetizing term of energy is not local. This brings some difficulties for the theoretical and numerical point of view. In the second part, we present the methods that we have implemented to solve the linear systems which appears in the simulation codes. We used a method of preconditionned conjugate gradient type and a method of expansion coupled with the former. In the third part, we prove that there is a finite number of singularities of the magnetization inside the material. For this, we use the theory introduced by Sch\oe n and Uhlenbeck for the functions which minimize the Dirichlet energy on the unite sphere. In particular, we had to take into account the non local characteristic of the demagnetizing energy.
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Christophe Bonjour. Inversion de systèmes linéaires pour la simulation des matériaux ferromagnétiques. Singularités d'une configuration d'aimantation. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1990. Français. ⟨tel-00004975⟩

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