Multiple right hand side multigrid for domain wall fermions with a preconditioned block conjugate gradient algorithm (2/8)

by Prof. Peter Boyle (Brookhaven National Laboratory)

Monday 28 Oct 2024, 15:00 → 16:00 Europe/Berlin

1.021 (ZOOM)

We introduce a class of efficient multiple right-hand side multigrid algorithm for domain wall fermions. The simultaneous solution for a modest number of right-hand sides concurrently allows for a significant reduction in the time spent solving the coarse grid operator in a multigrid preconditioner. We introduce a preconditioned block conjugate gradient with a multigrid preconditioner, giving additional algorithmic benefit from the multiple right-hand sides. The multiple right-hand sides also allows for a significant computation rate improvement. This both increases the arithmetic intensity in the coarse space and increases the amount of work being performed in each subroutine call, leading to excellent performance on modern GPU architectures. Further, the software implementation makes use of vendor linear algebra routines (batched GEMM) that can make use of high throughput tensor hardware on recent Nvidia, AMD and Intel GPUs. The cost of the coarse space is made sub-dominant in this algorithm, and benchmarks from the Frontier supercomputer system show up to a factor of twenty speed up over the standard red-black preconditioned conjugate gradient algorithm on a large system with physical quark masses.