Parallel performance of the coarse space linear vertex solver and low energy basis preconditioner for spectral/hp elements

Authors:
L. Grinberg;D. Pekurovsky;S. J. Sherwin;G. E. Karniadakis
Affiliations:
Brown University, Division of Applied Mathematics, 182 George St. Providence, RI 02912, United States;San Diego Supercomputing Center, University of California, San Diego 9500 Gilman Drive, La Jolla, CA 92093, United States;Imperial College of Science, Technology and Medicine, Department of Aeronautics, Prince Consort Road, South Kensington, London SW7 2BY, United Kingdom;Brown University, Division of Applied Mathematics, 182 George St. Providence, RI 02912, United States
Venue:
Parallel Computing
Year:
2009

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Abstract

The big bottleneck in scaling PDE-based codes to petaflop computing is scalability of effective preconditioners. We have developed and implemented an effective and scalable low energy basis preconditioner (LEBP) for elliptic solvers, leading to computational savings of an order of magnitude with respect to other preconditioners. The efficiency of LEBP relies on the implementation of parallel matrix-vector multiplication required by coarse solver to handle the h-scaling. We provide details on optimization, parallel performance and implementation of the coarse grain solver and show scalability of LEBP on the IBM Blue Gene and the Cray XT3.