Applications of semi-implicit Fourier-spectral method to phase field equations
Applications of semi-implicit Fourier-spectral method to phase field equations
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DOI：
10.1016/s0010-4655(97)00115-x
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发表时间：
1998-02-01
影响因子：
6.3
通讯作者：
Shen, J
中科院分区：
文献类型：
--
作者：
Chen, LQ;Shen, J
本文给出了求解含时Ginzburg-Landau方程和Cahn-Hilliard方程的一种有效而精确的数值方法。时间变量的离散化，使用半隐式计划，允许更大的时间步长比显式计划;空间变量的离散化，使用傅立叶谱方法，其收敛速度是指数的对比，由一个通常的有限差分法的二阶。通过求解含时的Ginzburg-Landau方程，我们应用我们的方法预测了定常平面界面上序参量的平衡态分布和运动界面的速度，并将我们的结果的精度和效率与其他人的结果进行了比较.我们证明，对于指定的精度为0.5%，使用半隐式傅立叶谱方法的加速比，显式有限差分格式相比，在二维中至少是两个数量级，在三维中接近三个数量级。该方法被证明是特别强大的系统中的形态和微观结构是由长程弹性相互作用为主。(C)1998年Elsevier Science B.V.
An efficient and accurate numerical method is implemented for solving the time-dependent Ginzburg-Landau equation and the Cahn-Hilliard equation. The time variable is discretized by using semi-implicit schemes which allow much larger time step sizes than explicit schemes; the space variables are discretized by using a Fourier-spectral method whose convergence rate is exponential in contrast to second order by a usual finite-difference method. We have applied our method to predict the equilibrium profiles of an order parameter across a stationary planar interface and the velocity of a moving interface by solving the time-dependent Ginzburg-Landau equation, and compared the accuracy and efficiency of our results with those obtained by others. We demonstrate that, for a specified accuracy of 0.5%, the speedup of using semi-implicit Fourier-spectral method, when compared with the explicit finite-difference schemes, is at least two orders of magnitude in two dimensions, and close to three orders of magnitude in three dimensions. The method is shown to be particularly powerful for systems in which the morphologies and microstructures are dominated by long-range elastic interactions. (C) 1998 Elsevier Science B.V.