Accelerating the Hybrid Monte Carlo algorithm with ILU preconditioning

TL;DR

This paper introduces an ILU preconditioning technique for the Hybrid Monte Carlo algorithm, significantly reducing computational costs by enabling larger step-sizes through reduced stochastic noise, demonstrated on the two-flavour Schwinger model.

Contribution

It presents a novel ILU preconditioning method integrated into HMC for dynamical fermions, improving efficiency over standard approaches.

Findings

Step-size increased by a factor of two with ILU preconditioning

Reduced stochastic noise in the pseudofermion action

Demonstrated effectiveness on the two-flavour Schwinger model

Abstract

The pseudofermion action of the Hybrid Monte Carlo (HMC) algorithm for dynamical fermions is modified to directly incorporate Incomplete LU (ILU) factorisation. This reduces the stochastic noise and allows a larger molecular dynamics step-size to be taken, cutting the computational cost. Numerical tests using the two-flavour Schwinger model are presented, where a two-step ILU preconditioning of the even-odd fermion matrix allows the step-size to be increased by a factor of two over the standard even-odd formulation.