Accelerating multigrid with streaming chiral SVD for Wilson fermions in lattice QCD

TL;DR

This paper introduces a streaming chiral SVD method to improve multigrid preconditioning for Wilson fermions in lattice QCD, enhancing convergence and reducing iteration counts, especially on resource-limited hardware.

Contribution

It presents a novel streaming SVD approach to optimize multigrid setup, significantly improving solver efficiency for Wilson fermions in lattice QCD.

Findings

Increased convergence speed with larger test vector basis.

Reduced iteration count by a factor of 1.7 using streaming SVD.

Demonstrated effectiveness on anisotropic and isotropic lattices.

Abstract

A modification to the setup algorithm for the multigrid preconditioner of Wilson fermions in lattice QCD is presented. A larger basis of test vectors than that used in conventional multigrid is calculated by the smoother and truncated by singular value decomposition on the chiral components of the test vectors. The truncated basis is used to form the prolongation and restriction matrices of the multigrid hierarchy. This modification of the setup method is demonstrated to increase the convergence of linear solvers 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. Increasing the number of test vectors improves speedup up to a point, but storing these vectors becomes impossible in limited memory resources such as GPUs. To address storage cost, we implement a \emph{streaming} singular value decomposition of the basis of test vectors on the chiral components and demonstrate a decrease in the number of fine level iterations by a factor of 1.7 for $m_q \approx m_{crit}$.