On vectorizing the preconditioned generalized conjugate residual methods

Abstract

A numerical study of the efficiency of the vectorized generalized conjugate residual methods (GCR) is performed using three different preconditioners, incomplete LU factorization, diagonal scaling and polynomial. The GCR behaviour is valued in connection with the solution of large, sparse unsymmetric systems of equations, arising from the finite element integration of the diffusion-convection equation. The size of the test problems ranges from 509 to 1700. Results from a set of numerical experiments are presented. The speed-up obtained is up to 11 times over the best scalar implementation. All the experiments were carried out on the vector computer Cray X-MP/48.

Keywords:

• Linear system
• generalized conjugate residual method
• preconditioners
• vector computers