C.-M. Pfeiler, D. Praetorius, M. Ruggeri,B. Stiftner:

"Linear second order implicit-explicit time integration of the (eddy-currents-) Landau-Lifschitz-Gilbert equation";

Talk: 13th Austrian Numerical Analysis Day, Salzburg; 2017-05-04 - 2017-05-05.

Combining ideas from [Praetorius et al. (arXiv 1611.02465)] and [Alouges et al. (Numer. Math., 128, 2014)], we present a numerical integrator for the integration of the Landau-Lifschitz Gilbert equation which is unconditionally convergent and formally (almost) second order in time, but requires only the solution of one linear system per time-step. Moreover, only the exchange contribution is treated implicitly in time, while the lower-order contributions like the computationally expensive stray field are treated explicitly in time. Moreover, we extend the scheme to the coupling of the Landau-Lifschitz Gilbert equation with eddy-currents. Unlike existing integrators for this PDE system, the new integrator is unconditionally convergent and (almost) second order in time and requires only the solution of two linear systems per time-step.

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