  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
Chebyshev-accelerated Schwarz and Jacobi preconditioning schemes is presented,
with special focus on GPU architectures, such as OLCF's Summit. Convergence
properties of the Chebyshev-accelerated 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 Krylov-subspace
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.
