  We propose a three-dimensional micromagnetic model that dynamically solves
the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion
equation. In contrast to previous methods, we solve for the magnetization
dynamics and the electric potential in a self-consistent fashion. This
treatment allows for an accurate description of magnetization dependent
resistance changes. Moreover, the presented algorithm describes both spin
accumulation due to smooth magnetization transitions and due to material
interfaces as in multilayer structures. The model and its finite-element
implementation are validated by current driven motion of a magnetic vortex
structure. In a second experiment, the resistivity of a magnetic multilayer
structure in dependence of the tilting angle of the magnetization in the
different layers is investigated. Both examples show good agreement with
reference simulations and experiments respectively.
