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arXiv · 1711.10715

Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation

Giovanni Di Fratta·Carl-Martin Pfeiler·Dirk Praetorius·Michele Ruggeri·Bernhard Stiftner
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Abstract

Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and [Praetorius et al. (Comput. Math. Appl., 2017)], 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 only the solution of 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 Landau-Lifshitz-Gilbert equation with the eddy current approximation of Maxwell equations (ELLG). Unlike existing schemes for this system, the new integrator is unconditionally convergent, (almost) second-order in time, and requires only the solution of two linear systems per time-step.

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Giovanni Di Fratta, Carl-Martin Pfeiler, Dirk Praetorius, Michele Ruggeri, Bernhard Stiftner. 2017-11-29. Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation. https://doi.org/10.1093/imanum%2Fdrz046

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