Speaker
Description
Efficient solutions of large sparse linear systems arising in lattice quantum chromodynamics (LQCD) are essential for modern numerical simulations. In this work, we investigate the use of a direct solver, based on ScaLAPACK, as the coarsest-level solver within the DDalphaAMG software package. Instead of performing an iterative solve on the coarsest grid of the multigrid hierarchy, we employ a direct factorization at this level.
This modification renders the multigrid preconditioner effectively stationary, which is advantageous for Krylov methods and substantially simplifies the treatment of multiple right-hand sides. The direct coarse solve avoids repeated coarse-level iterations and provides a reusable factorization for subsequent solves.
Current performance results indicate that the proposed method achieves solve times competitive with state-of-the-art LQCD solvers. Ongoing work focuses on the optimization of coarse-grid parameters and data distributions in order to further reduce the cost of the direct coarse solve and improve overall scalability.
These results demonstrate that a direct coarsest-level solver is a promising strategy for stationary multigrid preconditioning in LQCD and can provide an efficient framework for applications involving many right-hand sides within the DDalphaAMG software package.