Gauge fixing using overrelaxation and simulated annealing on GPUs

TL;DR

This paper demonstrates how GPUs can be effectively used for gauge fixing in lattice gauge theories, employing overrelaxation and simulated annealing algorithms to improve performance and accuracy.

Contribution

It introduces a GPU-optimized implementation of gauge fixing algorithms with high parallel efficiency and enhanced global maximum attainment through simulated annealing preconditioning.

Findings

Achieved ~300 GFlops performance on NVIDIA GTX 580

Parallel implementation with 8 threads per lattice site improves efficiency

Simulated annealing increases likelihood of reaching the global maximum

Abstract

We adopt CUDA-capable Graphic Processing Units (GPUs) for Coulomb, Landau and maximally Abelian gauge fixing in 3+1 dimensional SU(3) lattice gauge field theories. The local overrelaxation algorithm is perfectly suited for highly parallel architectures. Simulated annealing preconditioning strongly increases the probability to reach the global maximum of the gauge functional. We give performance results for single and double precision. To obtain our maximum performance of ~300 GFlops on NVIDIA's GTX 580 a very fine grained degree of parallelism is required due to the register limits of NVIDIA's Fermi GPUs: we use eight threads per lattice site, i.e., one thread per SU(3) matrix that is involved in the computation of a site update.