On preconditioned Krylov subspace methods for discrete convection–diffusion problems

We study nonstationary iterative methods for solving preconditioned systems arising from discretizations of the convection–diffusion equation. The preconditioners arise from Gauss–Seidel methods applied to the original system. It is shown that the performance of the iterative solvers is affected by the relationship of the ordering of the underlying grid and the direction of the fow associated with the differential operator. Specifically, only those orderings that follow the fow give fast iterative solvers. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13 :321–330