An incomplete-factorization preconditioning using repeated red-black ordering

Abstract

The convergence of the conjugate gradient method for the iterative solution of large systems of linear equations depends on proper preconditioning matrices. We present an efficient incomplete-factorization preconditioning based on a specific, "repeated red-black" ordering scheme and cyclic reduction. For the Dirichlet model problem, we prove that the condition number increases asymptotically slower with the number of equations than for usual incomplete factorization methods. Numerical results for symmetric and non-symmetric test problems and on locally refined grids demonstrate the performance of this method, especially for large linear systems.