【摘要】 KSSO LV(Kohn-Sham Solver)是一款用于求解平面波基组下Kohn-Sham方程(KS-DFT)的MATLAB (Matrix Laboratory)工具箱.在KS-DFT的基态计算中,通常自洽场迭代中Kohn-Sham哈密顿量的对角化是最昂贵的部分.为了使得个人计算机也能够执行数百个原子的中等大小KS-DFT计算,本文提出了一种CPUGPU的混合编程方案,通过调用MATLAB内置的并行计算工具箱来加速在KSSOLV中实现的迭代对角化算法.比较了 KSSOLV-GPU在RTX3090、V100、A100三种GPU上的性能;结果表明,对于包含128个原子的块状硅体系,与串行的CPU计算相比,混合CPU-GPU的编程可以实现约10倍的加速.特别是其在最新的民用GPU显卡RTX3090上也具有优秀的表现,可以预想到在不远的将来,KSSOLV-GPU借助MATLAB强大的可视化能力与GPU的加速支持可以在一台配备了民用GPU显卡的个人电脑上实现常规的D FT计算分析与可视化,从而降低了材料模拟与计算领域的门槛.更多还原

【Abstract】 KSSOLV(Kohn-Sham Solver) is a MATLAB(Matrix Laboratory) toolbox for solving the Kohn-Sham density functional theory(KS-DFT)with the plane-wave basis set. In the KS-DFT calculations, the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field(SCF) scheme. To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms, we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox. We compare the performance of KSSOLV-GPU on three types of GPU, including RTX3090, V100, and A100, with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.更多还原