A parallel algorithm for the partial eigensolution of sparse symmetric matrices on the CRAY Y-MP

doi:10.1016/S0167-8191(05)80156-5

Parallel Computing

Volume 17, Issues 4–5, July 1991, Pages 553-561

https://doi.org/10.1016/S0167-8191(05)80156-5 Get rights and content

Abstract

A parallel algorithm for the calculation of the p leftmost eigenpairs of large, sparse F.E.M. matrices is presented. Test problems are carried out on symmetric, positive definite matrices whose dimensions range from N = 222 to N = 4560. The method, which is intrinsically parallel, is based on the simultaneous minimization of the Rayleigh quotient obtained using an appropriate preconditioned version of the conjugate gradient scheme. The parallel implementation on a CRAY Y-MP8/432 supercomputer is described. The computational efficiency is evaluated with different test matrices and CPU number varying from 1 to 4. The average parallel speedups obtained with 2, 3, and 4 processors are respectively 1.72, 2.24, 2.63. They suggest that a high percentage of the code is efficiently parallelized.

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A parallel algorithm based on the multidimensional minimization of the Rayleigh quotient is proposed to evaluate the leftmost eigenpairs of the generalized symmetric positive definite eigenproblem. The minimization is performed via a conjugate gradient-like procedure accelerated by a factorized approximate inverse preconditioner (FSAI) and by a number of block preconditioners. The resulting code obtains a high level of parallel efficiency and proves to be comparable with the PARPACK package on a set of large matrices arising from various discretizations of PDEs of elliptic/parabolic type.
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2000, Numerical Linear Algebra with Applications
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1994, Numerical Methods for Partial Differential Equations
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^*: Work supported in part by CNR-GNIM and CNR-Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo

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Practical aspects and experiencesA parallel algorithm for the partial eigensolution of sparse symmetric matrices on the CRAY Y-MP*

Abstract

Parallel Comput.

J. Comput. Phys.

J. Comput. Phys.

Parallel Comput.

Parallel Comput.

Parallel Comput.

Adv. Water Resources

J. Comput. Phys.

Parallel Comput.

Solution methods for eigenvalue problems in structural mechanics

Internat. J. Numer. Methods Engrg.

Practical aspects and experiences
A parallel algorithm for the partial eigensolution of sparse symmetric matrices on the CRAY Y-MP*