发表机构
College of Computing, Georgia Institute of Technology; Department of Mathematics, Emory University; College of Engineering, Georgia Institute of Technology; Physics Division, Lawrence Livermore National Laboratory（佐治亚理工学院计算学院; 埃默里大学数学系; 佐治亚理工学院工程学院; 劳伦斯利弗莫尔国家实验室物理部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于Lanczos求积和插值的无矩阵实空间RPA关联能计算方法，实现高度并行，在4096核上30分钟内以化学精度计算256价电子硅体系。
AI 中文摘要
我们提出了一种高度可并行、无矩阵的实空间方法，用于在Kohn-Sham密度泛函理论框架内计算随机相位近似（RPA）关联能。具体而言，我们避免了响应函数矩阵的显式构造和特征分解，并利用Lanczos求积在实空间网格上评估矩阵函数的迹。我们还展示了利用RPA关联能密度在实空间中的空间平滑性来降低计算成本的可能性。具体来说，我们在粗网格上计算能量密度，然后通过插值重建全细网格的近似值。我们在SPARC电子结构软件包中实现了该公式，并展示了其收敛性、准确性、与平面波结果的一致性以及扩展性。插值可将计算预因子降低8倍。鉴于所提方法具有令人尴尬的并行性，我们实现了接近理想的加速比和接近三次方的扩展性，从而使得我们能够在4096个CPU核心上，在不到30分钟内，以化学精度计算具有256个价电子的硅体系的RPA关联能。
英文摘要
We present a highly parallelizable, matrix-free, real-space method for computing the random phase approximation (RPA) correlation energy within Kohn-Sham density functional theory. In particular, we avoid the explicit construction and eigen-decomposition of the response function matrix and use Lanczos quadrature to evaluate the trace of a matrix function on a real-space grid. We also show it is possible to exploit the spatial smoothness of the RPA correlation energy density in real-space to reduce computational cost. Specifically, we compute the energy density on a coarse grid, then reconstruct an approximation to the full, fine grid via interpolation. We implement this formulation within the SPARC electronic structure package and demonstrate its convergence, accuracy, agreement with planewave results, and scaling. Interpolation can enable an $8\times$ reduction in the computational prefactor. Given the embarrassingly parallel nature of the proposed method, we achieve near-ideal speedups and near-cubic scaling, thus allowing us to compute the RPA correlation energy for a silicon system with 256 valence electrons at chemical accuracy in less than 30 minutes on 4,096 CPU cores.
Comments21 pages, 4 figures, 4 tables
