Reduced Systems for Three-Dimensional Elliptic Equations with Variable Coefficients

Abstract

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