Optimizing Staggered Multigrid for Exascale performance

TL;DR

This paper evaluates and enhances staggered multigrid algorithms for lattice gauge theory, demonstrating significant performance improvements on supercomputers by offloading multi-shift solves to multigrid methods.

Contribution

It analyzes the performance of staggered multigrid algorithms in four dimensions and introduces offloading techniques that improve efficiency in high-performance computing environments.

Findings

Multigrid algorithms show remarkable success for staggered fermions.

Offloading multi-shift solves to multigrid significantly boosts performance.

Performance gains are demonstrated on Summit and Selene supercomputers.

Abstract

Adaptive multi-grid methods have proven very successful in dealing with critical slow down for the Wilson-Dirac solver in lattice gauge theory. Multi-grid algorithms developed for Staggered fermions using the K\"ahler-Dirac preconditioning~\cite{Brower:2018ymy} have shown remarkable success. In this work, we discuss the performance of this staggered multi-grid algorithm in four dimensions. We also demonstrate that offloading some components of a multi-shift solve to a multi-grid solver leads to a significant performance improvement in an existing MILC spectrum workflow on the Summit and Selene supercomputers.