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

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