An Unconditionally Energy Stable Method for the Anisotropic Phase-Field Crystal Model in Two Dimension

This paper explores efficient numerical approximations for the anisotropic phase-field crystal model in two dimension, aiming to analyze lattice systems characterized by varying anisotropic parameters and orientations. Some linear and fully decoupled schemes are constructed for this model in accordance with the Lagrange multiplier approach, that dissipate the original energy rather than the modified energy. Unlike the scalar auxiliary variable method, the newly developed technique does not necessitate the nonlinear term of the energy to have a lower bound. This approach is highly easy-to-implement, we solve two sixth-order linear equations with constant coefficients and a nonlinear algebraic equation just requiring a few Newton-type iterations at each time step. Some numerical simulations demonstrate the accuracy, the mass conservation and the energy dissipation of the proposed schemes.