GaDE -- GPU-acceleration of time-dependent Dirac Equation for exascale

TL;DR

GaDE is a GPU-accelerated solver for the 3D time-dependent Dirac equation, optimized for distributed HPC systems, demonstrating high scalability and performance on exascale architectures for relativistic quantum simulations.

Contribution

This paper introduces GaDE, a novel GPU-accelerated solver for the Dirac equation that efficiently utilizes MPI and CUDA/HIP for scalable electron dynamics simulations in relativistic regimes.

Findings

Achieves 85% parallel efficiency on 2048 GPUs

Demonstrates 16x speedup with 50% efficiency on 32 GPUs

Performs comparably on NVIDIA A100 and AMD MI250X GPUs

Abstract

Modern heterogeneous high-performance computing (HPC) systems powered by advanced graphics processing unit (GPU) architectures enable accelerating computing with unprecedented performance and scalability. Here, we present a GPU-accelerated solver for the three-dimensional (3D) time-dependent Dirac equation optimized for distributed HPC systems. The solver named GaDE is designed to simulate the electron dynamics in atoms induced by electromagnetic fields in the relativistic regime. It combines MPI with CUDA/HIP to target both NVIDIA and AMD GPU architectures. We discuss our implementation strategies in which most of the computations are carried out on GPUs, taking advantage of the GPU-aware MPI feature to optimize communication performance. We evaluate GaDE on the pre-exascale supercomputer LUMI, powered by AMD MI250X GPUs and HPE's Slingshot interconnect. Single-GPU performance on NVIDIA A100, GH200, and AMD MI250X shows comparable performance between A100 and MI250X in compute and memory bandwidth, with GH200 delivering higher performance. Weak scaling on LUMI demonstrates exceptional scalability, achieving 85% parallel efficiency across 2048 GPUs, while strong scaling delivers a 16x speedup on 32 GPUs - 50% efficiency for a communication-intensive, time-dependent Dirac equation solver. These results demonstrate GaDE's high scalability, making it suitable for exascale systems and enabling predictive simulations for ultra-intense laser experiments probing relativistic quantum effects.