Volume 56, Number 4, July-August 2022
|Page(s)||1199 - 1222|
|Published online||27 June 2022|
Numerical analysis of the Landau–Lifshitz–Gilbert equation with inertial effects
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK
* Corresponding author: firstname.lastname@example.org
Accepted: 26 April 2022
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.
Mathematics Subject Classification: 35K61 / 65M12 / 65M60 / 65Z05
Key words: Finite element method / inertial Landau–Lifshitz–Gilbert equation / micromagnetics
© The authors. Published by EDP Sciences, SMAI 2022
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