Optimization of the Oktay-Kronfeld Action Conjugate Gradient Inverter

TL;DR

This paper enhances the efficiency of the Oktay-Kronfeld action's conjugate gradient inverter through optimization and GPU acceleration, significantly speeding up calculations for heavy quark system spectra and weak matrix elements.

Contribution

It introduces optimized GPU-based implementations of the conjugate gradient inverter for the Oktay-Kronfeld action, achieving substantial speedups in lattice QCD computations.

Findings

Increased inverter speed by a factor of four on MILC coarse lattices.

GPU acceleration of gauge link matrix multiplications by over an order of magnitude.

Potential for further improvements using QUDA library.

Abstract

Improving the Fermilab action to third order in heavy quark effective theory yields the Oktay-Kronfeld action, a promising candidate for precise calculations of the spectra of heavy quark systems and weak matrix elements relevant to searches for new physics. We have optimized the bi-stabilized conjugate gradient inverter in the SciDAC QOPQDP library and are developing a GPU code. The action is rewritten and the needed gauge-link combinations are precalculated. In tests with a MILC coarse lattice, this procedure accelerates the inverter by a factor of four. The remaining floating-point operations are mostly simple matrix multiplications between gauge links and fermion vectors, which we accelerate by more than an order of magnitude by using CUDA. Further gains could be achieved by using QUDA.