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SUMMARY:Numerical Analysis for the Stochastic Landau-Lifshitz-Gilbert equa
 tion - Prohl\, A (Universitt Tbingen)
DTSTART:20120913T101000Z
DTEND:20120913T110000Z
UID:TALK39728@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION: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 inequali
 ty\, and construct weak martingale solutions of the limiting problem for v
 anishing discretization parameters. \n\nThen\, we study long-time dynamics
  of the space discretization of SLLG. The system is shown to relax exponen
 tially fast to the unique invariant measure (Boltzmann)\, as well as the c
 onvergent space-time discretization. \n\nComputational results for SLLG wi
 ll be discussed to evidence the role of noise\, including avoidance of fin
 ite time blow-up behavior of solutions of the related deterministic proble
 m\, and the study of long-time dynamics. \n\nThis is joint work with L. Ba
 nas (Edinburgh)\, Z. Brzezniak (York)\, and M. Neklyudov (Tuebingen). \n\n
LOCATION:Seminar Room 1\, Newton Institute
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