Reduced systems for three-dimensional elliptic equations with variable coefficients

We consider large sparse nonsymmetric linear systems arising from finite di fference discretization of three-dimensional (3D) convection-diffusion equa tions with variable coefficients. We show that performing one step of cycli c reduction yields a system of equations which is well conditioned and for which fast convergence can be obtained. A certain block ordering strategy i s applied, and analytical results concerning symmetrizability conditions an d bounds on convergence rates are given. The analysis is accompanied by num erical examples.