论文标题
铁电薄膜中相变的变异相位场模型的数值离散化
Numerical Discretization of Variational Phase Field Model for Phase Transitions in Ferroelectric Thin Films
论文作者
论文摘要
相位场方法已被广泛用于研究铁电薄膜中的相变和极化切换。在本文中，我们基于静电能的变异形式和极化载体的弛豫动力学开发了一个有效的数值方案。空间离散化结合了傅立叶光谱法与有限差异方法，以处理三维混合边界条件。它允许有效的半无限制离散化，以使放松动力学的时间整合。该方法避免明确求解静电平衡方程（泊松方程），并消除了相关的Lagrange乘数的使用。我们提出了几个数值示例，包括相变和极化切换过程，以证明该方法的有效性。
Phase field methods have been widely used to study phase transitions and polarization switching in ferroelectric thin films. In this paper, we develop an efficient numerical scheme for the variational phase field model based on variational forms of the electrostatic energy and the relaxation dynamics of the polarization vector. The spatial discretization combines the Fourier spectral method with the finite difference method 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 present several numerical examples including phase transitions and polarization switching processes to demonstrate the effectiveness of the proposed method.
