L. Banas, M. Page, D. Praetorius, J. Rochat:

"On the Landau-Lifshitz-Gilbert equations with magnetostriction";

IMA J. Numer. Anal.,34(2014), 4; S. 1361 - 1385.

To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system

of the nonlinear Landau-Lifshitz-Gilbert equation and the conservation of momentum

equation. This coupling allows to include magnetostrictive effects into the simulations.

Existence of weak solutions has recently been shown in [CARBOU ET AL., Math. Meth. Appl.

Sci. (2011)]. In our contribution, we give an alternate proof which additionally provides an

effective numerical integrator. The latter is based on linear finite elements in space and a

linear-implicit Euler time-stepping. Despite the nonlinearity, only two linear systems have to

be solved per timestep, and the integrator fully decouples both equations. Finally, we prove

unconditional convergence-at least of a subsequence-towards, and hence existence of, a

weak solution of the coupled system, as timestep size and spatial mesh-size tend to zero. We

conclude the work with numerical experiments which study the discrete blow-up of the LLG

equation as well as the influence of the magnetostrictive term on the discrete blow-up.

LLG, magnetostriction, linear scheme, ferromagnetism, convergence.

http://dx.doi.org/10.1093/imanum/drt050

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.