Solving Lattice QCD systems of equations using mixed precision solvers on GPUs

TL;DR

This paper demonstrates how mixed precision solvers on GPUs can efficiently solve lattice QCD systems, achieving high performance and accuracy by combining different precision levels in Krylov methods.

Contribution

The authors introduce a novel mixed precision approach for Krylov solvers that maintains double precision accuracy while leveraging faster single and half precision computations.

Findings

GPU implementations reach up to 212 Gflops for half precision

Mixed precision solvers outperform defect-correction methods in iteration count

Full double precision accuracy achieved with reduced computational cost

Abstract

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40 Gflops, 135 Gflops and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.