In this paper, we consider numerical approximations for the anisotropic phase-field crystal model. The model is a sixth-order nonlinear equation with an anisotropic Laplace operator. To develop easy-to-implement and unconditionally energy stable time marching schemes, we combine the scalar auxiliary variable (SAV) approach with the stabilization method, where two extra stabilization terms are added to enhance the stability and keep the required accuracy while using large time steps. By using the first-order backward Euler and second-order backward differentiation formula, we obtain two highly efficient and linear numerical schemes and prove their unconditional energy stabilities rigorously. We demonstrate the accuracy, stability, and efficiency of the developed schemes through numerous benchmark numerical experiments.

在本文中，我们考虑了各向异性相场晶体模型的数值近似。该模型是带有各向异性Laplace算子的六阶非线性方程。为了开发易于实现且无条件的能量稳定时间行进方案，我们将标量辅助变量（SAV）方法与稳定方法相结合，其中添加了两个额外的稳定项以增强稳定性并在使用大量时间的同时保持所需的精度脚步。通过使用一阶反向欧拉和二阶反向微分公式，我们获得了两个高效的线性数值方案，并严格证明了它们的无条件能量稳定性。我们通过大量的基准数值实验证明了所开发方案的准确性，稳定性和效率。