@Article{NMTMA-17-1041,
author = {Gui , YanDu , Rui and Wang , Cheng},
title = {A Third-Order Implicit-Explicit Runge-Kutta Method for Landau-Lifshitz Equation with Arbitrary Damping Parameters},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2024},
volume = {17},
number = {4},
pages = {1041--1073},
abstract = {<p style="text-align: justify;">A third-order accurate implicit-explicit Runge-Kutta time marching numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with arbitrary damping parameters. This method has three remarkable advantages: (1) only
a linear system with constant coefficients needs to be solved at each Runge-Kutta
stage, which greatly reduces the time cost and improves the efficiency; (2) the optimal rate convergence analysis does not impose any restriction on the magnitude
of damping parameter, which is consistent with the third-order accuracy in time for
1-D and 3-D numerical examples; (3) its unconditional stability with respect to the
damping parameter has been verified by a detailed numerical study. In comparison
with many existing methods, the proposed method indicates a better performance
on accuracy and efficiency, and thus provides a better option for micromagnetics
simulations.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2024-0036 },
url = {http://global-sci.org/intro/article_detail/nmtma/23651.html}
}