基于两级Chebyshev滤波器的互补子空间方法：推进大规模电子结构计算
Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations
摘要：
我们描述了一种新的迭代策略Kohn-Sham密度泛函理论计算的目的是大系统（> 1000电子），适用于金属和绝缘体一样。在每次自洽场（SCF）迭代时，我们采用基于两级Chebyshev多项式滤波器的互补子空间策略来代替显式对角化的Kohn-Sham哈密顿量：1）计算一组跨越哈密顿量的占用子空间的向量; 2）将子空间对角化减少到仅部分占用状态;以及3）经由内部切比雪夫滤波器迭代以有效的、可缩放的方式获得那些状态。通过将必要的计算减少到仅部分占据的状态，并通过内部切比雪夫迭代获得这些状态，我们的方法显着降低了大型金属计算的成本，同时完全消除了绝缘系统的子空间对角化。我们描述的不连续Galerkin（DG）的电子结构方法的框架内的方法的实施，并表明，这导致在一个计算方案，可以有效地解决散装和纳米系统包含数以万计的电子，化学精度，在几分钟或更少的挂钟时间每个SCF迭代在大规模的计算平台。我们预计，我们的方法将有助于推动大规模从头算分子动力学的信封。作为演示，我们模拟了一个含有8,000个原子的体硅系统在有限的温度下，并获得一个平均SCF步骤壁时间为51秒的34,560处理器，从而使我们能够进行1.0 ps的从头算分子动力学在大约28小时（壁时间）。
英文摘要：
We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to: 1) compute a set of vectors that span the occupied subspace of the Hamiltonian; 2) reduce subspace diagonalization to just partially occupied states; and 3) obtain those states in an efficient, scalable manner via an inner Chebyshev-filter iteration. By reducing the necessary computation to just partially occupied states, and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the Discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 hours (of wall time).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
