This thesis presents an adaptive wavelet method for the simulation of the time evolution of the magnetization of nanoelements and the results obtained with the numerical simulations.
The evolution of the magnetization (m) of a nanoelement situated in a non-magnetic medium is modeled mathematically with the Landau-Lifshitz equation. One term in that equation, the demagnetizing field, is derived from the solution of a Poisson equation whose right hand side depends on m. Of these two equations, coupled via the magnetization, the first one is discretized by a pointwise Euler scheme while the other is solved with an adaptive wavelet method.
The multi-level features of wavelet bases are used to cope with the sharp variations in the magnetization strength at the interface between the nano-element (where 1ml = 1) and the surrounding non-magnetic region (where 1ml = 0), and in the magnetization direction within the nanoelement, which may occur under certain circumstances with the formation of narrow domain walls. The aim of the adaptive scheme is to make maximum use of an
affordable number of degrees of freedom by concentrating the computational resources in the locations where the sharpest variations in m are situated. The challenge for such a method is to ensure that the size of the memory and the number of operations remains proportional to the number of degrees of freedom.