  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.
