Abstract
In this paper, we consider numerical approximations for the magnetic-coupled phase-field-crystal model for ferromagnetic solid materials. The governing PDE system consists of two coupled and highly nonlinear equations in which one is the Cahn–Hilliard equation for the density of atoms, and the other is the Allen–Cahn equation for the magnetization field. To solve it, we construct an unconditionally energy stable scheme with the second-order accuracy in time based on the recently developed stabilized-SAV approach. The energy stability of the scheme is proved, and the stability and accuracy are then demonstrated numerically by implementing various numerical examples in 2D and 3D, including the crystal growth and phase separations for both of the magnetic-free and magnetic-coupled cases.
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