  We present a simple and fast method to simulate spin-torque driven
magnetisation dynamics in nano-pillar spin-valve structures. The approach is
based on the coupling between a spin transport code based on random matrix
theory and a micromagnetics finite-elements software. In this way the spatial
dependence of both spin transport and magnetisation dynamics is properly taken
into account. Our results are compared with experiments. The excitation of the
spin-wave modes, in- cluding the threshold current for steady state
magnetisation precession and the nonlinear frequency shift of the modes are
reproduced correctly. The giant magneto resistance effect and the magnetisa-
tion switching also agree with experiment. The similarities with recently
described spin-caloritronics devices are also discussed.
