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Parallel Preconditioning for CFD Problems on the CM-5Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.
Document ID
20010122939
Acquisition Source
Ames Research Center
Document Type
Conference Paper
Authors
Simon, Horst D.
(Computer Sciences Corp. Moffett Field, CA United States)
Kremenetsky, Mark D.
(Thinking Machines Corp. Moffett Field, CA United States)
Richardson, John
(Thinking Machines Corp. Moffett Field, CA United States)
Lasinski, T. A.
Date Acquired
August 20, 2013
Publication Date
January 1, 1994
Subject Category
Fluid Mechanics And Thermodynamics
Meeting Information
Meeting: International Workshop on Solution Techniques for Large-Scale CFD Problems
Location: Montreal, Quebec
Country: Canada
Start Date: September 26, 1994
End Date: September 28, 1994
Funding Number(s)
PROJECT: RTOP 536-01-11
CONTRACT_GRANT: NAS2-12961
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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