Numerical Discretization of Variational Phase Field Model for Phase Transitions in Ferroelectric Thin Films (Communications in Computational Physics, 2021)
Phase field methods have been widely used to study phase transitions andpolarization switching in ferroelectric thin films. In this paper, we develop an efficientnumerical scheme for the variational phase field model based on variational forms ofthe electrostatic energy and the relaxation dynamics of the polarization vector. Thespatial discretization combines the Fourier spectral method with the finite differencemethod to handle three-dimensional mixed boundary conditions. It allows for an efficient semi-implicit discretization for the time integration of the relaxation dynamics.This method avoids explicitly solving the electrostatic equilibrium equation (a Poisson equation) and eliminates the use of associated Lagrange multipliers. We presentseveral numerical examples including phase transitions and polarization switchingprocesses to demonstrate the effectiveness of the proposed method.