SC12 Home > SC12 Schedule > SC12 Presentation - Norm-Coarsened Ordering for Parallel Incomplete Cholesky Preconditioning

SCHEDULE: NOV 10-16, 2012

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Norm-Coarsened Ordering for Parallel Incomplete Cholesky Preconditioning

SESSION: ACM Student Research Competition Poster Session

EVENT TYPE: ACM Student Research Competition

TIME: 5:15PM - 7:00PM

SESSION CHAIR: Torsten Hoefler

AUTHOR(S):Joshua D. Booth

ROOM:East Entrance

The preconditioned conjugate gradient method using incomplete Cholesky factors (PCG-IC) is a widely used iterative method for the scalable parallel solution of linear systems with a sparse symmetric positive definite coefficient matrix. Performance of the method depends on the ordering of the coefficient matrix which controls fill-in, exposes parallelism, and changes the convergence of conjugate gradient method. Furthermore, for a truly parallel solution, it is desirable that the ordering step itself can be parallelized. Earlier work indicates that orderings such as nested dissection and coloring that are suitable for parallel solution can often degrade the quality of the preconditioner. This work seeks to address this gap by developing a norm-coarsened ordering scheme that can be implemented in parallel while potentially improving convergence. Norm-coarsened ordering may improve the effective flops (iterations times nonzeros in the preconditioner) by as much 68% compared to nested dissection orderings and 34% compared to Reverse Cuthill-McKee.

Chair/Author Details:

Torsten Hoefler (Chair) - ETH Zurich

Joshua D. Booth - Pennsylvania State University

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