Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model.
Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model.
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DOI：
10.1103/physreve.76.056706
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发表时间：
2007-02
期刊：
影响因子：
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通讯作者：
B. Athreya;N. Goldenfeld;J. Dantzig;M. Greenwood;N. Provatas
中科院分区：
文献类型：
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作者：
B. Athreya;N. Goldenfeld;J. Dantzig;M. Greenwood;N. Provatas
我们实现了一个自适应网格算法，用于计算微观材料过程中原子密度场的空间和时间依赖性。我们的数值方法使用系统的重整化群配方的相场晶体模型的纯材料提供的基本方程的复杂振幅的原子密度场-一个数量是空间均匀的，除了附近的拓扑缺陷，晶界，和其他晶格缺陷。我们的算法采用混合制定的振幅方程，结合笛卡尔和极分解的复振幅。我们表明，这种方法导致加速三个数量级的多晶晶粒生长在两个维度的模型计算。
We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field in microscopic material processes. Our numerical approach uses the systematic renormalization-group formulation of a phase-field crystal model of a pure material to provide the underlying equations for the complex amplitude of the atomic density field--a quantity that is spatially uniform except near topological defects, grain boundaries, and other lattice imperfections. Our algorithm employs a hybrid formulation of the amplitude equations, combining Cartesian and polar decompositions of the complex amplitude. We show that this approach leads to an acceleration by three orders of magnitude in model calculations of polycrystalline grain growth in two dimensions.