相场晶元模型振幅展开的高效数值框架
An efficient numerical framework for the amplitude expansion of the phase-field crystal model
AI总结：
本文提出了一种高效的数值框架，用于解决相场晶元模型的振幅展开问题，通过有限元方法在实空间中进行计算，并开发了优化的预条件器和基于局部旋转的网格自适应准则，以模拟大规模三维系统中的多尺度特性。
摘要：
多晶材料的研究需要理论和计算技术，以实现多尺度研究。相场晶元模型（APFC）的振幅展开允许在扩散时间尺度上描述晶体晶格特性，通过关注在原子间距大于的长度尺度上变化的连续场。因此，它允许在保留晶格细节的情况下模拟大规模系统。受该方法应用的推动，本文提出了一种高效的数值框架来求解其方程。特别是，我们考虑了一种利用有限元方法的实空间方法。开发了一个优化的预条件器，以提高线性求解器的收敛性。此外，基于局部旋转的多晶网格自适应准则被使用。这导致了模拟大规模三维系统的能力，包括多晶材料中微结构的动力学描述及其位错网络。
英文摘要：
The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on diffusive timescales by focusing on continuous fields varying on length scales larger than the atomic spacing. Thus, it allows for the simulation of large systems still retaining details of the crystal lattice. Fostered by the applications of this approach, we present here an efficient numerical framework to solve its equations. In particular, we consider a real space approach exploiting the finite element method. An optimized preconditioner is developed in order to improve the convergence of the linear solver. Moreover, a mesh adaptivity criterion based on the local rotation of the polycrystal is used. This results in an unprecedented capability of simulating large, three-dimensional systems including the dynamical description of the microstructures in polycrystalline materials together with their dislocation networks.
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