Non-periodic finite-element formulation of Kohn–Sham density functional theory
Non-periodic finite-element formulation of Kohn–Sham density functional theory
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DOI：
10.1016/j.jmps.2009.10.002
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发表时间：
2010-02
影响因子：
5.3
通讯作者：
Phanish Suryanarayana;V. Gavini;T. Blesgen;K. Bhattacharya;M. Ortiz
中科院分区：
文献类型：
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作者：
Phanish Suryanarayana;V. Gavini;T. Blesgen;K. Bhattacharya;M. Ortiz
我们提出了一个实空间，非周期性，有限元制定Kohn-Sham密度泛函理论（KS-DFT）。我们将原变分问题转化为一个局部鞍点问题，并通过证明极小点的存在性来证明其适定性。此外，我们证明了有限元逼近，包括数值求积的收敛性。区域分解的基础上，我们开发了一个并行的有限元实现这个配方能够进行全电子和赝势计算。我们评估的准确性，制定通过选定的测试案例，并表现出良好的协议与文献。我们还评估了其可扩展性和收敛速度方面的实现的数值性能。我们认为这项工作是朝着开发一种方法迈出的一步，该方法可以使用密度泛函理论（DFT）以合理的计算成本准确地研究空位，位错和裂纹尖端等缺陷，在必要时保持电子分辨率，并在远处无缝粗粒化。
We present a real-space, non-periodic, finite-element formulation for Kohn–Sham density functional theory (KS-DFT). We transform the original variational problem into a local saddle-point problem, and show its well-posedness by proving the existence of minimizers. Further, we prove the convergence of finite-element approximations including numerical quadratures. Based on domain decomposition, we develop a parallel finite-element implementation of this formulation capable of performing both all-electron and pseudopotential calculations. We assess the accuracy of the formulation through selected test cases and demonstrate good agreement with the literature. We also evaluate the numerical performance of the implementation with regard to its scalability and convergence rates. We view this work as a step towards developing a method that can accurately study defects like vacancies, dislocations and crack tips using density functional theory (DFT) at reasonable computational cost by retaining electronic resolution where it is necessary and seamlessly coarse-graining far away.