Tuning Spectral Element Preconditioners for Parallel Scalability on GPUs
Malachi Phillips, Stefan Kerkemeier, Paul Fischer · Society for Industrial and Applied Mathematics eBooks · 2022
The Poisson pressure solve resulting from the spectral element discretization of the incompressible Navier-Stokes equation requires fast, robust, and scalable preconditioning. In the current work, a parallel scaling study of Chebyshevaccelerated Schwarz and Jacobi preconditioning schemes is presented, with special focus on GPU architectures, such as OLCF's Summit. Convergence properties of the Chebyshevaccelerated schemes are compared with alternative methods, such as low-order preconditioners combined with algebraic multigrid. Performance and scalability results are presented for a variety of preconditioner and solver settings. The authors demonstrate that Chebyshev-accelerated-Schwarz methods provide a robust and effective smoothing strategy when using p-multigrid as a preconditioner in a Krylovsubspace projector. The variety of cases to be addressed, on a wide range of processor counts, suggests that performance can be enhanced by automated run-time selection of the preconditioner and associated parameters.