Chronological Inversion Method for the Dirac Matrix in Hybrid Monte Carlo

TL;DR

This paper introduces a method to improve Dirac matrix inversion in Hybrid Monte Carlo simulations by using a superposition of past solutions, significantly reducing computational effort.

Contribution

It proposes a novel chronological inversion method that leverages past solutions to accelerate Dirac matrix inversion in lattice QCD simulations.

Findings

Number of conjugate gradient iterations halved

Method reduces computational cost in HMC simulations

Extensions to preconditioning discussed

Abstract

In Hybrid Monte Carlo simulations for full QCD, the gauge fields evolve smoothly as a function of Molecular Dynamics time. Here we investigate improved methods of estimating the trial or starting solutions for the Dirac matrix inversion as superpositions of a chronological sequence of solutions in the recent past. By taking as the trial solution the vector which minimizes the residual in the linear space spanned by the past solutions, the number of conjugate gradient iterations per unit MD time is decreased by at least a factor of 2. Extensions of this basic approach to precondition the conjugate gradient iterations are also discussed.