We present a simple and fast method to simulate spin-torque driven magnetization dynamics in nanopillar 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 magnetization dynamics is properly taken into account. Our results are compared with experiments. The excitation of the spin-wave modes, including the threshold current for steady-state magnetization precession and the nonlinear frequency shift of the modes are reproduced correctly. The giant magneto resistance effect and the magnetization switching also agree with experiment. The similarities with recently described spin-caloritronics devices are also discussed.