MRHS multigrid solver for Wilson-clover fermions

TL;DR

This paper presents a multigrid solver for Wilson-clover fermions that leverages multiple right-hand sides to enhance parallelism, achieving significant speedups on GPU-based supercomputers.

Contribution

The implementation of a multigrid solver for Wilson-clover fermions using MRHS to improve parallelism across diverse architectures with detailed performance benchmarks.

Findings

10x speedup on 16 GPUs for a $24^3\times128$ lattice

Effective parallelism increase by solving multiple right-hand sides

Benchmarks on Nvidia A100 GPUs demonstrate high efficiency

Abstract

We describe our implementation of a multigrid solver for Wilson-clover fermions, which increases parallelism by solving for multiple right-hand sides (MRHS) simultaneously. The solver is based on Grid and thus runs on all computing architectures supported by the Grid framework. We present detailed benchmarks of the relevant kernels, such as hopping and clover term on the various multigrid levels, intergrid operators, and reductions. The benchmarks were performed on the JUWELS Booster system at J\"ulich Supercomputing Centre, which is based on Nvidia A100 GPUs. For example, solving a $24^3\times128$ lattice on 16 GPUs, the overall speedup obtained solely from MRHS is about 10x.