Second-order semi-implicit projection methods for micromagnetics simulations
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Micromagnetics simulations require accurate approximation of the magnetiza- tion dynamics described by the Landau-Lifshitz-Gilbert equation, which is non- linear, nonlocal, and has a non-convex constraint, posing interesting challenges in developing numerical methods. In this paper, we propose two second-order semi-implicit projection methods based on the second-order backward differen- tiation formula and the second-order interpolation formula using the informa- tion at previous two temporal steps. Unconditional unique solvability of both methods is proved, with their second-order accuracy verified through numerical examples in both 1D and 3D. The efficiency of both methods is compared to that of another two popular methods. In addition, we test the robustness of both methods for the first benchmark problem with a ferromagnetic thin film material from National Institute of Standards and Technology.