Numerical simulation of the microwave behavior of ferromagnetic materials
During the 40's, W.F. Brown introduced the micromagnetism theory to explain the behaviour of non-linear magnetic materials : the ferro and ferrimagnetics. The model used is based on two main points. The first one is the use of the Landau-Lifchitz partial differential equation, which describes the evolution in time of the magnetisation.The second one is the integration of internal stress as a magnetic excitation. This excitation is composed of four parts : external, anisotropy, exchange and demagnetisation (magnetostatic). It is this last contribution that induces the greatest difficulties in modelisation. In this work, the simulation of ferro and ferrimagnetic material behaviour in the microwave domain is studied. Two aspects are focused on : the determination of equilibrium states and the computation of microwave susceptibility. First of all, the existence of weak solutions in time and space is proved. A resolution scheme is proposed for the Landau-Lifchitz equations. This scheme is explicit and an adaptative time step is used. One of the goals is to apply the scheme to very large cubic meshes. A fast solving method for huge matrices is proposed based upon the use of block-Toeplitz matrices to resolve the magnetostatic problem. Finally, a preconditonning method is developed improving the resolution of the susceptibility problem (i.e. response computation for an external harmonic excitation). Finally, numerical results are validate by comparison with a set of experimental results.