A Second-Order Operator Splitting Fourier Spectral Method for Models of Epitaxial Thin Film Growth
A Second-Order Operator Splitting Fourier Spectral Method for Models of Epitaxial Thin Film Growth
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DOI：
10.1007/s10915-016-0340-4
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发表时间：
2017-01
影响因子：
2.5
通讯作者：
H. Lee;Jaemin Shin;June-Yub Lee
中科院分区：
文献类型：
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作者：
H. Lee;Jaemin Shin;June-Yub Lee
本文发展了一种算子分裂傅立叶谱方法，用于研究有斜率选择和无斜率选择的外延薄膜生长模型。该方法的主要思想是将原方程分解为线性和非线性两部分，然后将一步演化分为三个子步。线性部分由谱方法求解，该方法在傅立叶空间中具有封闭形式的解。非线性部分也用谱方法结合Crank-Nicolson型方法求解。我们数值计算表明，我们的方法在空间上达到了谱精度，在时间上达到了二阶精度，并且消除了对时间步长的限制。我们还进行了长时间的模拟粗化过程中显示的能力的方法。
In this paper, we develop an operator splitting Fourier spectral method for models of epitaxial thin film growth with and without slope selection. A main idea of the method is to split the original equation into linear and nonlinear parts, and then to evolve one step which consists of three substeps. The linear part is solved by the spectral method, which has a closed-form solution in the Fourier space. And the nonlinear part is also solved by the spectral method combined with the Crank–Nicolson type method. We numerically demonstrate that our method achieves spectral accuracy in space and second-order accuracy in time and alleviates restriction on the time step. We also perform long time simulations for the coarsening process to show the capability of the method.