Load balancing of parallel block overlapped incomplete cholesky preconditioning

Abstract

A modification of the second order Incomplete Cholesky (IC) factorization with controllable amount of fill-in is described and analyzed. This algorithm is applied to the construction of well balanced coarse-grain parallel preconditioning for the Conjugate Gradient (CG) iterative solution of linear systems with symmetric positive definite matrix. The efficiency of the resulting parallel algorithm is illustrated by a series of numerical experiments using large-scale ill-conditioned test matrices taken from the collection of the University of Florida. © 2009 Springer Berlin Heidelberg.