Adaptive multigrid algorithm for the lattice Wilson-Dirac operator

TL;DR

This paper introduces an adaptive multigrid solver tailored for the non-Hermitian Wilson-Dirac system in QCD, effectively reducing critical slowing down and maintaining performance across different lattice volumes.

Contribution

The paper presents a novel adaptive multigrid algorithm that preserves the near null space and exploits gamma_5-Hermitian symmetry for efficient solutions of the Wilson-Dirac operator.

Findings

Nearly eliminates critical slowing down in the chiral limit

Weak dependence on lattice volume

Effective for non-Hermitian Wilson-Dirac systems

Abstract

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called gamma_5-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.