Implementation of the Neuberger-Dirac operator on GPUs

TL;DR

This paper presents a GPU implementation of the Neuberger-Dirac operator for lattice QCD simulations, achieving significant speed-ups that facilitate studies of Ginsparg-Wilson fermions and related decay processes.

Contribution

The work introduces an efficient GPU-based implementation of the Neuberger-Dirac operator, including exact low-mode treatment, with benchmarks demonstrating substantial performance gains.

Findings

Achieved speed-up factors of ~23 (single precision) and ~16 (double precision).

Enabled more efficient lattice QCD simulations involving Ginsparg-Wilson fermions.

Facilitated studies of decay processes like K → ππ.

Abstract

Recent developments have shown that a lot can be gained for QCD simulations from GPU hardware. This can be exploited especially in the case of Ginsparg-Wilson fermions when the com putational costs are particularly high. In this work, we use the Neuberger-Dirac operator as our realisation of Ginsparg-Wilson fermions, which greatly facilitate lattice investigations of decays like $K \to \pi\pi$. We report on the ongoing study of our GPU implementation of the Neuberger-Dirac operator including the exact treatment of the low lying eigenmodes of the Wilson-Dirac operator. Our benchmarks show that we achieve speed-up factors of around 23 and 16 in single and double precision, respectively.