An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
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DOI：
10.1137/100812781
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发表时间：
2011-05
期刊：
影响因子：
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通讯作者：
Zhonghua Qiao;Zhengru Zhang;T. Tang
中科院分区：
文献类型：
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作者：
Zhonghua Qiao;Zhengru Zhang;T. Tang
本文对分子束外延（MBE）模型的动力学过程进行了数值模拟。分子束外延模型的数值模拟需要较长的计算时间，因此需要大的时间步长方法。在这篇文章中，我们考虑了一些无条件能量稳定的有限差分格式，这些格式将用于时间自适应策略。结果表明，利用时间自适应性不仅可以准确有效地求解稳态解，而且可以准确有效地求解动态变化解。自适应时间步长的选择是基于能量的变化或粗糙度的变化的解决方案。数值实验表明，对于长时间的模拟，CPU时间显着节省。
This paper is concerned with the numerical simulations for the dynamics of the molecular beam epitaxy (MBE) model. The numerical simulations of the MBE models require long time computations, and therefore large time-stepping methods become necessary. In this work, we consider some unconditionally energy stable finite difference schemes, which will be used in the time adaptivity strategies. It is found that the use of the time adaptivity cannot only resolve the steady-state solutions but also the dynamical changes of the solution accurately and efficiently. The adaptive time step is selected based on the energy variation or the change of the roughness of the solution. The numerical experiments demonstrated that the CPU time is significantly saved for long time simulations.