Extrapolation Methods for the Dirac Inverter in Hybrid Monte Carlo

TL;DR

This paper explores advanced extrapolation techniques for the Dirac inverter in Hybrid Monte Carlo simulations, significantly reducing computational effort by leveraging past trajectory data to improve solver efficiency.

Contribution

It introduces improved extrapolation methods that utilize previous solutions to enhance the Dirac inverter's performance in HMC simulations.

Findings

Reduced CG iterations by a factor of 4 with current methods

Potential for further efficiency gains with more trajectory data

Improved solver performance in full QCD simulations

Abstract

In Hybrid Monte Carlo(HMC) simulations for full QCD, the gauge fields evolve smoothly as a function of Molecular Dynamics (MD) time. Thus we investigate improved methods of estimating the trial solutions to the Dirac propagator as superpositions of the solutions in the recent past. So far our best extrapolation method reduces the number of Conjugate Gradient iterations per unit MD time by about a factor of 4. Further improvements should be forthcoming as we further exploit the information of past trajectories.