  We numerically analyze the possibility of turning off post-smoothing
(relaxation) in geometric multigrid when used as a preconditioner in conjugate
gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric
Semicoarsening Multigrid (SMG) method is provided by the hypre parallel
software package. We solve linear systems using two variants (standard and
flexible) of the preconditioned conjugate gradient (PCG) and preconditioned
steepest descent (PSD) methods. The eigenvalue problems are solved using the
locally optimal block preconditioned conjugate gradient (LOBPCG) method
available in hypre through BLOPEX software. We observe that turning off the
post-smoothing in SMG dramatically slows down the standard PCG-SMG. For
flexible PCG and LOBPCG, our numerical results show that post-smoothing can be
avoided, resulting in overall acceleration, due to the high costs of smoothing
and relatively insignificant decrease in convergence speed. We numerically
demonstrate for linear systems that PSD-SMG and flexible PCG-SMG converge
similarly if SMG post-smoothing is off. We experimentally show that the effect
of acceleration is independent of memory interconnection. A theoretical
justification is provided.
