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Numerical Analysis for the Stochastic Landau-Lifshitz-Gilbert equation

Prohl, A (Universität Tübingen)
Thursday 13 September 2012, 11:10-12:00

Seminar Room 1, Newton Institute


Thermally activated magnetization dynamics is modelled by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). A finite element based space-time discretization is proposed, where iterates conserve the unit-length constraint at nodal points of the mesh, satisfy an energy inequality, and construct weak martingale solutions of the limiting problem for vanishing discretization parameters.

Then, we study long-time dynamics of the space discretization of SLLG. The system is shown to relax exponentially fast to the unique invariant measure (Boltzmann), as well as the convergent space-time discretization.

Computational results for SLLG will be discussed to evidence the role of noise, including avoidance of finite time blow-up behavior of solutions of the related deterministic problem, and the study of long-time dynamics.

This is joint work with L. Banas (Edinburgh), Z. Brzezniak (York), and M. Neklyudov (Tuebingen).


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