A Comparison of Preconditioned Nonsymmetric Krylov Methods on a Large-Scale MIMD Machine

Shadid, John N.; Tuminaro, Ray S.

doi:10.1137/0915030

A Comparison of Preconditioned Nonsymmetric Krylov Methods on a Large-Scale MIMD Machine

Conference · Wed Jan 01 19:00:00 EST 1992 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/0915030· OSTI ID:6014096

Shadid, John N. ^[1]; Tuminaro, Ray S. ^[1]

Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Many complex physical processes are modeled by coupled systems of partial differential equations (PDEs). Often, the numerical approximation of these PDEs requires the solution of large sparse nonsymmetric systems of equations. In this paper we compare the parallel performance of a number of preconditioned Krylov subspace methods on a large-scale MIMD machine. These methods are among the most robust and efficient iterative algorithms for the solution of large sparse linear systems. They are easy to implement on various architectures and work well on a wide variety of important problems. In this comparison we focus on the parallel issues associated with both local preconditioners (those that combine information from the entire domain). The various preconditioners are applied to a variety of PDE problems within the GMRES, CCGS, BiCGSTAB, and QMRCGS methods. Conclusions are drawn on the effectiveness of the different schemes based on results obtained from a 1024 processor a nCUBE 2 hypercube.

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Energy Research (ER)

DOE Contract Number:: AC04-76DP00789

OSTI ID:: 6014096

Report Number(s):: SAND--91-0333C; CONF-920472--1; ON: DE92006838

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 2 Vol. 15; ISSN 1064-8275; ISSN 1095-7197

Publisher:: Society for Industrial and Applied Mathematics (SIAM)

Country of Publication:: United States

Language:: English

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99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
COMPARATIVE EVALUATIONS
COMPUTERS
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
HYPERCUBE COMPUTERS
ITERATIVE METHODS
KERNELS
Krylov methods
MATHEMATICAL LOGIC
MIMD
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
PROGRAMMING
linear systems
multilevel methods
nonsymmetric
parallel algorithms
preconditioners

A Comparison of Preconditioned Nonsymmetric Krylov Methods on a Large-Scale MIMD Machine

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