CaDS Seminar 2024 - Nov. 5

Dr. Gustavo Ramirez Hidalgo (SDL Quantum Materials)

Parallel Efficiency of Coarsest Grid Solvers in Multigrid

Abstract:

Multigrid methods find their way into many applications in scientific computing. Simulations in theoretical studies of the inner workings of nuclei, in particular, are bound by the use of supercomputers to speed them up. Multigrid methods have brought a way of pushing the computational boundaries in such large-scale simulations, and they open the possibility of scalably simulating at the exascale. Unfortunately, under certain extreme situations such as the use of many processes and/or very high condition of the linear systems to be solved, the time spent at the coarsest grid ends up representing most of the execution time in those multigrid solves. If the solver employed at the coarsest level is e.g. GMRES, in which case we see the appearance of many dot products, scalability is at risk. We discuss here different ways in which we can improve the scalability of multigrid solvers by focusing on the coarsest level.All of our implementations and tests are performed within our solver library DD-alphaAMG, a solver for large and sparse matrices emerging in lattice quantum chromodynamics, but these techniques are useful in any application where multigrid fails to scale due to coarsest-level restrictions.