TY - JOUR
T1 - A Third-Order Implicit-Explicit Runge-Kutta Method for Landau-Lifshitz Equation with Arbitrary Damping Parameters
AU - Gui , Yan
AU - Du , Rui
AU - Wang , Cheng
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1041
EP - 1073
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2024-0036 
UR - https://global-sci.org/intro/article_detail/nmtma/23651.html
KW - Landau-Lifshitz equation, implicit-explicit Runge-Kutta time discretization, third-order, linear systems with constant coefficients, arbitrary damping.
AB - <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>