副矩阵和GPU加速实现密度矩阵紧密结合
Abylay Katbashev1, Robert Schade2, Michael Lass2,3
1Mulliken Center for Theoretical Chemistry, Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany.
The Journal of chemical physics
|October 2, 2025
概括
我们使用图形处理单元 (GPU) 和子矩阵方法开发了更快的紧密结合计算. 这加快了大型系统的模拟,使先进的计算材料科学更容易获得.
科学领域:
- 计算材料科学科学 计算材料科学
- 量子化学 是一个量子化学.
- 固态物理 固态物理
背景情况:
- 像Hartree-Fock和DFT这样的单粒子理论面临着由于自相一致场 (SCF) 程序的立方缩放的计算限制.
- 没有先进的算法和硬件,大规模应用是不切实际的.
- 在这个领域,PTB紧固结合潜力是关键的方法.
研究的目的:
- 实施和评估GPU加速和子矩阵方法用于PTB紧密结合潜力.
- 克服传统SCF程序的计算瓶.
- 为了实现更大,更复杂的材料系统的模拟.
主要方法:
- 与密度矩阵净化方法对比传统的基于对角化的SCF溶解器.
- 实施一种分解类型的子矩阵方法,以实现高效的计算.
- 使用图形处理单元 (GPU) 进行加速计算.
- 系统大小和计算机硬件的系统变化.
主要成果:
- GPU 加速实现了 10-15 倍的性能提速,使更大的系统的模拟成为可能.
- 亚矩阵方法减少了大约10^4基础函数的系统的计算成本.
- 通过子矩阵方法保持了可接受的数值准确性.
结论:
- GPU 加速和子矩阵方法的结合显著提高了紧密结合计算的效率.
- 这项工作推动了计算材料科学中可行的系统大小的边界.
- 这些发现强调了硬件-算法相互作用对未来发展的重要性.
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