Multigrid Algorithms for Domain-Wall Fermions

TL;DR

This paper introduces an adaptive multigrid algorithm tailored for domain-wall fermions, significantly reducing computational costs in lattice QCD simulations by efficiently handling near-null vectors and eliminating the fifth dimension in coarse spaces.

Contribution

The paper extends multigrid techniques to chiral fermion actions, specifically domain-wall fermions, by developing an adaptive projection method that reduces critical slowing and computational costs.

Findings

Near-elimination of critical slowing as quark mass decreases

Significant reduction in computational cost for domain-wall fermion inverses

Small volume dependence in the multigrid algorithm

Abstract

We describe an adaptive multigrid algorithm for solving inverses of the domain-wall fermion operator. Our multigrid algorithm uses an adaptive projection of near-null vectors of the domain-wall operator onto coarser four-dimensional lattices. This extension of multigrid techniques to a chiral fermion action will greatly reduce overall computation cost, and the elimination of the fifth dimension in the coarse space reduces the relative cost of using chiral fermions compared to discarding this symmetry. We demonstrate near-elimination of critical slowing as the quark mass is reduced and small volume dependence, which may be suppressed by taking advantage of the recursive nature of the algorithm.