Chiral rank-$k$ truncations for the multigrid preconditioner of Wilson fermions in lattice QCD

TL;DR

This paper introduces a chiral rank-$k$ truncation method for the multigrid preconditioner of Wilson fermions in lattice QCD, improving convergence by using a larger set of test vectors truncated via SVD.

Contribution

The paper proposes a novel modification to the multigrid setup algorithm that enhances convergence by employing chiral component truncation of test vectors.

Findings

Improved convergence on anisotropic and isotropic lattices.

Effective reduction of test vector set size without loss of performance.

Lattice volume dependence analyzed.

Abstract

We present a modification to the setup algorithm for the multigrid preconditioner of Wilson fermions in lattice QCD. A larger number of test vectors than that used in conventional multigrid is generated by the smoother. This set of test vectors is then truncated by a singular value decomposition on the chiral components of the test vectors, which are subsequently used to form the prolongation and restriction matrices of the multigrid hierarchy. This modification is demonstrated to improve the convergence of linear equations on an anisotropic lattice with $m_{\pi} \approx 239$ MeV from the Hadron Spectrum Collaboration and an isotropic lattice with $m_{\pi} \approx 220$ MeV from the MILC Collaboration. The lattice volume dependence of the method is also examined.