Second-order semi-implicit projection methods for micromagnetics simulations
arXiv:1907.02358 · doi:10.1016/j.jcp.2019.109104
Abstract
Micromagnetics simulations require accurate approximation of the magnetization dynamics described by the Landau-Lifshitz-Gilbert equation, which is nonlinear, 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 differentiation formula and the second-order interpolation formula using the information 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.
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Cited by in corpus (5)
- Numerical methods for antiferromagnetics
- A Gauss-Seidel projection method with the minimal number of updates for stray field in micromagnetic simulations
- Advantages of a semi-implicit scheme over a fully implicit scheme for Landau-Lifshitz-Gilbert equation
- A second-order semi-implicit method for the inertial Landau-Lifshitz-Gilbert equation
- A second-order numerical method for Landau-Lifshitz-Gilbert equation with large damping parameters