Affiliation:
1. Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstrasse 8–10, 1040 Vienna, Austria
Abstract
Abstract
Combining ideas from Alouges et al. (2014, A convergent and precise finite element scheme for Landau–Lifschitz–Gilbert equation. Numer. Math., 128, 407–430) and Praetorius et al. (2018, Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Comput. Math. Appl., 75, 1719–1738) we propose a numerical algorithm for the integration of the nonlinear and time-dependent Landau–Lifshitz–Gilbert (LLG) equation, which is unconditionally convergent, formally (almost) second-order in time, and requires the solution of only one linear system per time step. Only the exchange contribution is integrated implicitly in time, while the lower-order contributions like the computationally expensive stray field are treated explicitly in time. Then we extend the scheme to the coupled system of the LLG equation with the eddy current approximation of Maxwell equations. Unlike existing schemes for this system, the new integrator is unconditionally convergent, (almost) second-order in time, and requires the solution of only two linear systems per time step.
Funder
Austrian Science Fund
Vienna Science and Technology Fund
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,General Mathematics
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