In this paper, we consider numerical approximations for the anisotropic modified phasefield crystal model with a strong nonlinear vacancy potential, which describes microscopic phenomena involving atomic hopping and vacancy diffusion. The model is a nonlinear damped wave equation that includes an anisotropic Laplacian and a strong nonlinear vacancy term. To develop an easy to implement time marching scheme with unconditional energy stability, we combine the multiple scalar auxiliary variable (MSAV) approach with stabilization technique for achieving an efficient and linear numerical scheme, in which two new scalar auxiliary variables are introduced to reformulate the model and a linear stabilization term is added to enhance the stability and keep the required accuracy while using the large time steps. The scheme leads to decoupled linear equations with constant coefficients at each time step, and its unique solvability and unconditional energy stability are proved. Various numerical experiments are performed to show the accuracy, stability, and efficiency of the proposed scheme.

中文翻译：

---

具有强非线性空位势的各向异性修正相场晶体模型的高效数值方案

在本文中，我们考虑具有强非线性空位势的各向异性修正相场晶体模型的数值近似，该模型描述了涉及原子跳跃和空位扩散的微观现象。该模型是一个非线性阻尼波方程，其中包括各向异性拉普拉斯算子和强非线性空位项。为了开发一种易于实施且具有无条件能量稳定性的时间行进方案，我们将多标量辅助变量（MSAV）方法与稳定技术相结合，以实现高效且线性的数值方案，其中引入了两个新的标量辅助变量以重新编制模型并添加了线性稳定项，以增强稳定性并在使用较大时间步长的同时保持所需的精度。该方案导致在每个时间步长具有常数系数的解线性方程组，并且证明了其独特的可解性和无条件的能量稳定性。进行了各种数值实验，以显示所提出方案的准确性，稳定性和效率。