Mathematical and numerical studies of non linear ferromagnetic materials

In this paper we are interested in the numerical modeling of absorbing ferr omagnetic materials obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves. In thi s work we consider the ID problem. We first show that the corresponding Cau chy 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 pres erve some important properties of the continuous model such as the conserva tion of the norm of 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.