A finite-difference scheme for a model of magnetization dynamics with inertial effects

Moumni, M.; Tilioua, Mouhcine

doi:10.1007/s10665-015-9836-4

Cited by 4 publications

(1 citation statement)

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“…The proof is constructive and provides an alternative proof of existence of weak solutions to (1.2) (first established in [25]). The numerical analysis of iLLG has been considered so far only in [31], where a semi-implicit method has been proposed and its conservation properties have been analysed. The present work thus proposes the first numerical schemes that are proven to be convergent towards a weak solution of iLLG.…”

Section: Contributions and Outline Of The Present Workmentioning

confidence: 99%

Numerical analysis of the Landau–Lifshitz–Gilbert equation with inertial effects

Ruggeri

2022

ESAIM: M2AN

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We consider the numerical approximation of the inertial Landau–Lifshitz–Gilbert equation (iLLG), which describes the dynamics of the magnetisation in ferromagnetic materials at subpicosecond time scales. We propose and analyse two fully discrete numerical schemes: The first method is based on a reformulation of the problem as a linear constrained variational formulation for the linear velocity. The second method exploits a reformulation of the problem as a first order system in time for the magnetisation and the angular momentum. Both schemes are implicit, based on first-order finite elements, and generate approximations satisfying the unit-length constraint of iLLG at the vertices of the underlying mesh. For both methods, we prove convergence of the approximations towards a weak solution of the problem. Numerical experiments validate the theoretical results and show the applicability of the methods for the simulation of ultrafast magnetic processes.

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Section: Contributions and Outline Of The Present Workmentioning

confidence: 99%