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D. Praetorius, M. Ruggeri, B. Stiftner:
"Coupling and numerical integration of the Landau-Lifshitz-Gilbert equation";
Poster: Micromagnetics: Analysis, Numerics, Applications (MANA 2016), TU Wien, Vienna; 2016-02-18 - 2016-02-19.

The nonlinear Landau-Lifshitz-Gilbert (LLG) equation models the dynamics of the magnetization in ferromagnetic materials. Numerical challenges arise from strong nonlinearities, a nonconvex pointwise constraint which enforces length preservation, and the possible nonlinear coupling to other PDEs. We discuss numerical integrators, based on lowest-order FEM in space that are proven to be unconditionally convergent towards a weak solution of the problem. Emphasis is put on an effective numerical treatment, where the time-marching scheme decouples the numerical integration of the coupled equation. As an example, we consider the nonlinear coupling of the LLG equation with a diffusion equation which models the evolution of the spin accumulation in magnetic multilayers in the presence of electric current.