The present paper deals with a numerical analysis of the vectorization of the PCG (preconditioned conjugate gradient) method and PCGR (preconditioned generalized conjugate residual) methods. Three preconditioners are employed and analysed, incomplete factorization, diagonal scaling and polynomial. Their behaviour is evaluated in connection with the solution of large, sparse symmetric and unsymmetric systems of linear equations arising from the finite element integration of structural problems, subsurface flow problems and diffusion convection problems. The size of the test matrices ranges from 300 to 4500. In all the test problems, the vectorized implementation exhibits a speed-up larger than 2 with respect to the best scalar implementation. The numerical experiments have been performed on a Cray X-MP/48. The codes, wich make use of one CPU, are written in FORTRAN and are compiled by CFT.

On vectorizing gradient conjugate-like methods

GAMBOLATI, GIUSEPPE;PINI, GIORGIO;ZILLI, GIOVANNI
1989

Abstract

The present paper deals with a numerical analysis of the vectorization of the PCG (preconditioned conjugate gradient) method and PCGR (preconditioned generalized conjugate residual) methods. Three preconditioners are employed and analysed, incomplete factorization, diagonal scaling and polynomial. Their behaviour is evaluated in connection with the solution of large, sparse symmetric and unsymmetric systems of linear equations arising from the finite element integration of structural problems, subsurface flow problems and diffusion convection problems. The size of the test matrices ranges from 300 to 4500. In all the test problems, the vectorized implementation exhibits a speed-up larger than 2 with respect to the best scalar implementation. The numerical experiments have been performed on a Cray X-MP/48. The codes, wich make use of one CPU, are written in FORTRAN and are compiled by CFT.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2510125
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