Fast and stable explicit operator splitting methods for phase-field models
Fast and stable explicit operator splitting methods for phase-field models
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DOI：
10.1016/j.jcp.2015.09.005
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
Yuanzhen Cheng;A. Kurganov;Zhuolin Qu;T. Tang
中科院分区：
文献类型：
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作者：
Yuanzhen Cheng;A. Kurganov;Zhuolin Qu;T. Tang
相场模型的数值模拟需要长时间的计算，因此有必要发展高效、高精度的数值方法。在本文中，我们提出了快速和稳定的显式算子分裂方法的一维和二维非线性扩散方程的薄膜外延与斜率选择和Cahn-Hilliard方程。方程分为非线性部分和线性部分。非线性部分采用直线法和大稳定域显式常微分方程求解器求解。线性部分由伪谱方法求解，该方法基于精确解，因此对时间步长没有稳定性限制。我们证明了所提出的方法的性能上的一些一维和二维的数值例子，在不同阶段的粗化，如初始准备，交替快速结构转变和慢动作可以清楚地观察到。
Numerical simulations of phase-field models require long time computations and therefore it is necessary to develop efficient and highly accurate numerical methods. In this paper, we propose fast and stable explicit operator splitting methods for both one- and two-dimensional nonlinear diffusion equations for thin film epitaxy with slope selection and the Cahn–Hilliard equation. The equations are split into nonlinear and linear parts. The nonlinear part is solved using a method of lines together with an efficient large stability domain explicit ODE solver. The linear part is solved by a pseudo-spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. We demonstrate the performance of the proposed methods on a number of one- and two-dimensional numerical examples, where different stages of coarsening such as the initial preparation, alternating rapid structural transition and slow motion can be clearly observed.