Truncated incomplete factorizations for conjugate-gradient methods in two and three dimensions

摘要

Conjugate-gradient methods are very efficient when they are applied to preconditioned linear equation systems. Different degrees of truncation for incomplete factorization preconditioners are investigated. It is found that for solving Poisson's equation on curvilinear coordinate systems in two dimensions, generally all nine coefficients should be used for factorization, while in three dimensions a truncation which uses only the orthogonal directions is most efficient. For different grid resolutions in different directions the orientation of the coordinate system is important, which is confirmed by analyzing the eigenvalues of the preconditioned system.