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 atoms.