A second-order Strang splitting scheme for the generalized Allen-Cahn type phase-field crystal model with FCC ordering structure

In this paper, we consider the generalized Allen-Cahn-type phase -field crystal model with face -centered -cubic ordering structure (PFC-FCC). Due to the combined complexity of the eighth -order spatial derivative and inherent nonlinearity, it poses a significant challenge to design a numerical scheme of high accuracy, stability, and efficiency to solve the PFC-FCC model. Endeavoring towards this objective, we adopt operator splitting method to address the PFC-FCC model. Based on Fourier spectral method for spatial discretization and SSP-RK method for temporal discretization, we propose an effective and easy -to -implement secondorder scheme. We are also able to proffer an analytical proof for discrete mass conservation, and engage a discussion on an optimal error estimate for the second -order scheme. In addition, the energy stability of the numerical scheme is derived. Ultimately, a series of numerical experiments specifically designed to substantiate its accuracy, efficiency, and capability for phase transition are performed.