Computer Science NASC Seminar

Nonsymmetric Preconditioning for Symmetric Linear Equations and Eigenvalue Problems

Andrew Knyazev, Mitsubishi Electric Research Laboratories

November 08, 2013 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110

Fall 2013 NASC Seminars Calendar


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.
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 dramatically slows down the standard PCG. For the 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 converges nearly identical to flexible PCG if SMG post-smoothing is off. A theoretical justification is provided. [See {}]

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