In this paper, we propose a second-order fast explicit operator splitting method for the phase field crystal equation. The basic idea lied in our method is to split the original problem into linear and nonlinear parts. The linear subproblem is numerically solved using the Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. The nonlinear one is solved via second-order strong stability preserving Runge–Kutta method. The stability and convergence are discussed in \(L^2\)-norm. Numerical experiments are performed to validate the accuracy and efficiency of the proposed method. Moreover, energy degradation and mass conservation are also verified.

本文针对相场晶体方程提出了一种二阶快速显式算子分裂方法。我们的方法所隐含的基本思想是将原始问题分为线性和非线性部分。线性子问题使用傅立叶谱方法进行数值求解，该方法基于精确解，因此对时间步长没有稳定性的限制。非线性问题是通过二阶强稳定性保持Runge-Kutta方法求解的。\（L ^ 2 \）- norm中讨论了稳定性和收敛性。通过数值实验验证了所提方法的准确性和有效性。此外，还证实了能量降解和质量守恒。