A Gauss-Seidel projection method with the minimal number of updates for the stray field in micromagnetics simulations

Abstract

<p style='text-indent:20px;'>Magnetization dynamics in magnetic materials is often modeled by the Landau-Lifshitz equation, which is solved numerically in general. In micromagnetics simulations, the computational cost relies heavily on the time-marching scheme and the evaluation of the stray field. In this work, we propose a new method, dubbed as GSPM-BDF2, by combining the advantages of the Gauss-Seidel projection method (GSPM) and the second-order backward differentiation formula scheme (BDF2). Like GSPM, this method is first-order accurate in time and second-order accurate in space, and it is unconditionally stable with respect to the damping parameter. Remarkably, GSPM-BDF2 updates the stray field only once per time step, leading to an efficiency improvement of about <inline-formula><tex-math id="M1">\begin{document}$ 60\% $\end{document}</tex-math></inline-formula> compared with the state-of-the-art of GSPM for micromagnetics simulations. For Standard Problems #4 and #5 from National Institute of Standards and Technology, GSPM-BDF2 reduces the computational time over the popular software OOMMF by <inline-formula><tex-math id="M2">\begin{document}$ 82\% $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ 96\% $\end{document}</tex-math></inline-formula>, respectively. Thus, the proposed method provides a more efficient choice for micromagnetics simulations.</p>