Preconditioned iterative algorithms for large sparse unsymmetric problems

A numerical study of the efficiency of the generalized conjugate residual methods (GCR) is performed using three different preconditioners all based upon an incomplete LU factorization. The GCR behavior is evaluated in connection with the solution of large, sparse unsymmetric systems of equations, arising from the finite element integration of the diffusion-convection equation for 2-dimensional (2-D) and 3-D problems with different Peclet and Courant numbers. The order of the test matrices ranges from 450 to 1700. Results from a set of numerical experiments are presented and comparisons with preconditioned GCR methods and with direct method are carried out.