Efficient Shift-and-Invert Preconditioning for Multi-GPU Accelerated Density Functional Calculations,Journal of Chemical Theory and Computation

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Efficient Shift-and-Invert Preconditioning for Multi-GPU Accelerated Density Functional Calculations
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2024-08-27 , DOI: 10.1021/acs.jctc.4c00721
Jeheon Woo ₁ , Woo Youn Kim ₁ , Sunghwan Choi ₂

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To accelerate the iterative diagonalization of electronic structure calculations, we propose a new inexact shift-and-invert (ISI) preconditioning method. The key idea is to improve shift values in the ISI preconditioning to be closer to the exact eigenvalues, leading to a significant boost in the convergence speed of the iterative diagonalization. Furthermore, we adopted a preconditioned conjugate gradient solver to rapidly evaluate an inversion process. Finally, we accelerated overall processes, including the proposed modification, with state-of-the-art graphical processing units (GPUs) and assessed its parallel efficiency with real-space density functional calculations of 1D, 2D, and 3D periodic systems. Our method attains both fast diagonalization convergence and high multi-GPU parallel efficiency. This is evident from the fact that single-point density functional calculations for hundreds of atom systems can be done in approximately 10 s using 8 GPUs. The proposed method can be generally applied to any electronic structure calculation methods involving large-scale diagonalizations.

中文翻译：

用于多 GPU 加速密度泛函计算的高效移位和反转预处理

为了加速电子结构计算的迭代对角化，我们提出了一种新的不精确移位反转（ISI）预处理方法。关键思想是改进 ISI 预处理中的移位值，使其更接近精确的特征值，从而显着提高迭代对角化的收敛速度。此外，我们采用了预条件共轭梯度求解器来快速评估反演过程。最后，我们使用最先进的图形处理单元 (GPU) 加速了整个过程，包括所提出的修改，并通过 1D、2D 和 3D 周期系统的真实空间密度泛函计算评估了其并行效率。我们的方法实现了快速对角化收敛和高多 GPU 并行效率。从以下事实可以看出这一点：使用 8 个 GPU 在大约 10 秒内即可完成数百个原子系统的单点密度泛函计算。该方法可以普遍应用于任何涉及大规模对角化的电子结构计算方法。

更新日期：2024-08-27

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