Highly efficient and linear numerical schemes with unconditional energy stability for the anisotropic phase-field crystal model

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. (C) 2020 Elsevier B.V. All rights reserved.