A Novel Second-Order Scheme for the Molecular Beam Epitaxy Model with Slope Selection
A Novel Second-Order Scheme for the Molecular Beam Epitaxy Model with Slope Selection
复制标题
具有斜率选择的分子束外延模型的新型二阶方案
DOI：
10.4208/cicp.oa-2018-0015
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发表时间：
2019
影响因子：
3.7
通讯作者：
Gong Yuezheng
中科院分区：
文献类型：
--
作者：
Chen Lizhen;Zhao Jia;Gong Yuezheng
分子束外延（MBE）是材料科学中一个重要且具有挑战性的研究课题。在本文中，我们针对具有斜率选择的著名连续介质MBE模型提出了一种新的全离散格式。首先，我们使用多步法……（最后一个单词“stra”不完整，可能影响准确理解）
Molecular beam epitaxy (MBE) is an important and challenging research topic in material science. In this paper, we propose a new fully discrete scheme for the well-celebrated continuum MBE model with slope selection. First of all, we use a multi-step strategy to discretize the MBE model in time. The obtained semi-discrete scheme is proved to possess properties of total mass conservation, unconditionally energy stability and uniquely solvability. The rigorous error estimate is then conducted to show its second-order convergence. The semi-discrete scheme is further discretized in space using the Fourier pseudo-spectral method. The fully discrete scheme is also shown to preserve mass-conservation and energy-dissipation properties. Afterward, several numerical examples are presented to validate the accuracy and efficiency of our proposed scheme. In particular, the scaling law for the roughness growing and effective energy decaying are captured during long-time coarsening dynamic simulations. The idea proposed in this paper could be readily utilized to design accurate and stable numerical approximations for many other energy-based phase field models. AMS subject classifications: 65N22, 65M12, 65M70
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影响因子：
1.1
作者：
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影响因子：
2
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影响因子：
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DOI：
10.1137/110822839
发表时间：
2012
期刊：
SIAM J. Numer. Anal.
影响因子：
--
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影响因子：
2.5
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