Hybrid algorithms for cyclically reduced convection-diffusion problems

Abstract

We consider hybrid and adaptive iterative algorithms for cyclically-reduced discrete convection-diffusion problems. Hybrid algorithms combine via a two phase algorithm, iterative methods which require no a priori information about the coefficient matrix in the first phase with Chebyshev or Richardson iteration in the second phase. For two-dimensional convection-diffusion problems, central difference discretization is considered and the resulting linear system is reduced to approximately half its size by applying one step of cyclic reduction. We examine the numerical performance of the hybrid methods for solving the reduced systems. Our numerical experiments show that for the class of problems considered, an adaptive Chebyshev algorithm that uses modified moments to approximate the eigenvalues requires less work in most cases than the hybrid algorithms based on GMRES/Richardson methods.