arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1207.0167physics.comp-ph
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Kohn-Sham密度泛函理论的高阶自适应有限元方法

Higher-order adaptive finite-element methods for Kohn-Sham density functional theory

Phani Motamarri, Michael R Nowak, Kenneth Leiter, Jaroslaw Knap, Vikram Gavini

摘要:

我们提出了一种有效的计算方法来执行实空间电子结构计算使用自适应高阶有限元离散的Kohn-Sham密度泛函理论(DFT)。为此,我们开发了一个先验网格自适应技术,构建一个接近最佳的有限元离散化的问题。我们进一步提出了一个有效的解决方案,解决离散特征值问题,通过使用谱有限元结合高斯-洛巴托积分,和切比雪夫加速技术计算占用的特征空间。所提出的方法已被观察到提供了惊人的100-200倍的计算优势的广义特征值问题的解决方案。使用建议的解决方案的过程中,我们调查的计算效率提供高阶有限元离散的Kohn-Sham DFT问题。我们的研究表明,相对于线性有限元的1000倍的数量级惊人的计算节省可以实现,为所有电子和本地赝势计算。在所有的基准系统研究,我们观察到递减收益的计算节省超过六阶的准确性与化学准确性相称。对所提出的高阶有限元离散的计算效率的比较研究表明,对于非周期局部赝势计算,有限元基的性能与平面波离散相竞争,并且与高斯基的性能相比,对于全电子计算,有限元基的性能在一个数量级内。此外,我们证明了所提出的方法的能力,计算包含1688个原子的金属系统的电子结构,使用适度的计算资源,以及良好的可扩展性,本实施高达192个处理器。

英文摘要:

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a-priori mesh adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200 fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretization of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings of the order of 1000 fold relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.

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