Journal Article

FZJ-2026-02092

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Accelerating multigrid with streaming chiral SVD for Wilson fermions in lattice QCD

Whyte, T. (Corresponding author)FZJ* ; Stathopoulos, A. ; Romero, E.

2026
Elsevier B.V. Amsterdam

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Please use a persistent id in citations: doi:10.1016/j.cpc.2026.110089  doi:10.34734/FZJ-2026-02092

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 regular 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 $m_π ≈ 239 MeV$ from the Hadron Spectrum Collaboration and an isotropic lattice with $mπ ≈ 220 MeV$ 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 <i>streaming</i> 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 $m_q ≈ m_{crit}$.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5111 - Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups (POF4-511) (POF4-511)
2. SFB 1639 B02 - Gitterfeldtheorien an der Schwelle zur Exascale-Ära (B02) (537420013) (537420013)
3. DFG project G:(GEPRIS)511713970 - SFB 1639: NuMeriQS: Numerische Methoden zur Untersuchung von Dynamik und Strukturbildung in Quantensystemen (511713970) (511713970)

Appears in the scientific report 2026

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