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.
A parallel algorithm for the partial eigensolution of sparse symmetric matrices on the CRAY Y-MP
PINI, GIORGIO
1991
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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