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Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation
- Source :
- IMA Journal of Numerical Analysis, 40 (2020), 2802-2838
- Publication Year :
- 2017
-
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.
- Subjects :
- Mathematics - Numerical Analysis
Physics - Computational Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- IMA Journal of Numerical Analysis, 40 (2020), 2802-2838
- Publication Type :
- Report
- Accession number :
- edsarx.1711.10715
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1093/imanum/drz046