Block stationary methods for nonsymmetric cyclically reduced systems arising from three-dimensional elliptic equations

We consider a three-dimensional convection-diffusion model problem and exam ine systems of equations arising from performing one step of cyclic reducti on on an equally spaced mesh, discretized using the seven-point operator. W e present two ordering strategies and analyze block splittings of the resul ting matrices. If the matrices are consistently ordered relative to a given partitioning, Young's analysis for the block Gauss-Seidel and block SOR me thods can be applied. We compare partitionings for which this property hold s with ones where the matrices do not have Property A yet still give rise t o an efficient solution process. Bounds on convergence rates are derived an d the work involved in solving the systems is estimated.