P. Goldenits, G. Hrkac,M. Page, D. Praetorius, D. Süss:

"Convergent geometric integrator for the LLG equation with magnetostriction";

Poster: Analytical and Numerical Aspects of Evolution Equations, Bielefeld; 03-19-2012 - 03-23-2012.

The theoretical understanding and practical prediction of

micromagnetic phenomena is of utmost importance for the improvement

of existing and development of future magnetic based devices like

e.g. storage devices, sensors, or magnetic RAM. However, certain

aspects do not need the practical development of prototypes, but can

also be well understood by means of numerical simulations. This

relies on the mathematical modelling of micromagnetics. In physics,

it is well-accepted that the dynamics of micromagnetics is described

best by the nonlinear Landau-Lifshitz-Gilbert equation (LLG), where

time evolution is driven by the so-called effective field h_eff.

We propose a numerical time integrator that solves the LLG equation

even considering the five energy contributions exchange, anisotropy,

strayfield, exterior field, and magnetostrictive component for h_eff.

The latter couples LLG to the conservation of momentum equation. We

show that the proposed scheme leads to unconditional convergence as

(h,k) tend to (0,0) independently of each other. In addition, even

though we treat a nonlinearly coupled system of two PDEs, we only

have to solve two linear systems per timestep.

http://publik.tuwien.ac.at/files/PubDat_209366.pdf

Created from the Publication Database of the Vienna University of Technology.