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arXiv 1506.08147physics.comp-phphysics.chem-ph
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DGDFT:一种大规模并行密度泛函理论计算方法

DGDFT: A Massively Parallel Method for Large Scale Density Functional Theory Calculations

Wei Hu, Lin Lin, Chao Yang

摘要:

我们描述了一个大规模的并行实现最近开发的不连续伽辽金密度泛函理论(DGDFT)[J. COMPUT。2012,231,2140]方法,用于有效的大规模基于Kohn-Sham DFT的电子结构计算。DGDFT方法使用在自洽场(SCF)迭代期间动态生成的自适应局部基(ALB)函数来表示Kohn-Sham方程的解。ALB集的使用提供了一种系统的方法来提高近似的精度。它最大限度地减少了所需的自由度,以代表解决方案的科恩-沙姆问题所需的精度水平。特别地,DGDFT可以以少得多的自由度达到平面波精度。通过使用极展开和选择反演(PEXSI)技术计算电子密度、能量和原子力,我们可以使DGDFT的计算复杂度对于绝缘和金属系统都最多为电子数的二次方。我们表明,DGDFT可以实现80%的并行效率在128,000高性能计算核心时,它被用来研究二维(2D)磷烯系统的电子结构与3,500 - 14,000原子。这种高并行效率来自我们将详细描述的两级并行化方案。

英文摘要:

We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) [J. Comput. Phys. 2012, 231, 2140] method, for efficient large-scale Kohn-Sham DFT based electronic structure calculations. The DGDFT method uses adaptive local basis (ALB) functions generated on-the-fly during the self-consistent field (SCF) iteration to represent the solution to the Kohn-Sham equations. The use of the ALB set provides a systematic way to improve the accuracy of the approximation. It minimizes the number of degrees of freedom required to represent the solution to the Kohn-Sham problem for a desired level of accuracy. In particular, DGDFT can reach the planewave accuracy with far fewer numbers of degrees of freedom. By using the pole expansion and selected inversion (PEXSI) technique to compute electron density, energy and atomic forces, we can make the computational complexity of DGDFT scale at most quadratically with respect to the number of electrons for both insulating and metallic systems. We show that DGDFT can achieve 80% parallel efficiency on 128,000 high performance computing cores when it is used to study the electronic structure of two-dimensional (2D) phosphorene systems with 3,500-14,000 atoms. This high parallel efficiency results from a two-level parallelization scheme that we will describe in detail.

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