KSSOLV-GPU：一款利用GPU高效求解Kohn-Sham方程的平面波基组密度泛函理论MATLAB程序包

KSSOLV(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CPU-GPU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DFT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.

KSSOLV-GPU: an Efficient GPU-Enabled MATLAB Toolbox for Solving the Kohn-Sham Equations within Density Functional Theory in Plane-Wave Basis Set

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 atom.