# MRHS multigrid solver for Wilson-clover fermions

arXiv: https://arxiv.org/abs/2211.13719 · HTML: https://mlsanity.com/paper/2211.13719/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2022.

## Built on by (most cited first, 1 of 1)

- [Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory](https://mlsanity.com/paper/2509.10378/) (2025)

## Abstract (arXiv)

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 243×128 lattice on 16 GPUs, the overall speedup obtained solely from MRHS is about 10x.