Spin-polarized transport in ferromagnetic multilayers: An   unconditionally convergent FEM integrator
  We propose and analyze a decoupled time-marching scheme for the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation for the spin accumulation. This model describes the interplay of magnetization and electron spin accumulation in magnetic and non-magnetic multilayer structures. Despite the strong nonlinearity of the overall PDE system, the proposed integrator requires only the solution of two linear systems per time-step. Unconditional convergence of the integrator towards weak solutions is proved. 
Claas Abert, Gino Hrkac, Marcus Page, Dirk Praetorius, Michele   Ruggeri, Dieter Suess
math.NA physics.comp-ph