Time resolved micromagnetics using a preconditioned time integration method

A detailed description for the solution of the Landau-Lifshitz-Gilbert equation with the finite element method is given. The use of implicit time integration schemes with proper preconditioning is reported. Simulations of a single-phase magnetic nanoelement, without surface roughness and a magnetic nanoelement with a granular structure are performed to investigate the influence of the microstructure on the numerical behavior. Nanoelements with a granular structure cause an inhomogeneous computational grid. In granular systems preconditioning for time integration speeds up the simulations by three orders of magnitude as compared to conventional time integration schemes like the Adams method. (C) 2002 Elsevier Science B.V. All rights reserved.