Improving HISQ propagator solves using deflation

TL;DR

This paper explores the use of deflation techniques to improve the efficiency of HISQ propagator solves, addressing critical slowing down at physical quark masses, and compares it with multigrid methods.

Contribution

It demonstrates the effectiveness of deflation in reducing critical slowing down for HISQ propagator computations and compares it with multigrid approaches.

Findings

Deflation reduces critical slowing down in HISQ propagator solves.

Deflation incurs setup costs but improves solve times at physical quark masses.

Comparison shows trade-offs between deflation and multigrid methods.

Abstract

Typically, the conjugate gradient (CG) algorithm employs mixed precision and even-odd preconditioning to compute propagators for highly improved staggered quarks (HISQ). This approach suffers from critical slowing down as the light quark mass is decreased to its physical value. Multigrid is one alternative to combat critical slowing down; however, it involves setup costs that are not always easy to amortize. We consider deflation, which can also remove critical slowing down, but incurs its own setup cost to compute eigenvectors. Results using the MILC and QUDA software libraries to generate eigenvectors and to perform deflated solves on lattices up to $144^3 \times 288$ (with lattice spacing 0.04 fm) and with a range of quark masses from the physical strange down to the physical light quark values will be presented. We compare with CG and comment on deflation versus multigrid.