Acceleration ofthe Relativistic Dirac–Kohn–ShamMethod with GPU: A Pre-Exascale Implementation of BERTHA and PyBERTHA

In this paper, we present the recent advances in the computation of the Dirac–Kohn–Sham (DKS) method of the BERTHA code. We show here that the simple underlined structure of the FORTRAN code also favors efficient porting of the code to GPUs, leading to a particularly efficient hybrid CPU/GPU implementation (OpenMP/OpenACC), where the most computationally intensive part for DKS matrix evaluation (three-center two-electron integrals evaluated via the McMurchie–Davidson scheme) is efficiently offloaded to the GPU via compiler directives based on the OpenACC programming model. This scheme in combination with the use of a linear algebra library optimized for GPUs (cuBLAS, cuSOLVER) significantly accelerates the DKS calculations. In addition, the low-level integral kernel developed here at FORTRAN level was used to port our real-time DKS (RT-TDDKS) implementation based on Python (PyBERTHART) for the utilization of the GPU. The results obtained on the new Tier-0 EuroHPC supercomputer (LEONARDO) of the CINECA Supercomputing Centre with a single NVIDIA A100 card are very satisfactory. We achieve a speedup up to 30 for Au₁₆ in a single-point DKS energy calculation and up to 10 for the Au₈ systems in an RT-TDDKS calculation, compared to our OpenMP (i.e., CPU only) parallel implementation (with 32 cores). The approach presented here is very general and, to our knowledge, represents the first port of a Python API to GPUs based on a FORTRAN kernel for the evaluation of two-electron integrals. The implementation is currently limited to the use of a single GPU accelerator, but future paths to an actual exascale implementation are discussed.