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Scientific Programming
Volume 13 (2005), Issue 2, Pages 79-91

Parallel Preconditioned Conjugate Gradient Square Method Based on Normalized Approximate Inverses

George A. Gravvanis and Konstantinos M. Giannoutakis

Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, GR 67100 Xanthi, Greece

Received 1 December 2005; Accepted 1 December 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new class of normalized explicit approximate inverse matrix techniques, based on normalized approximate factorization procedures, for solving sparse linear systems resulting from the finite difference discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse matrix techniques for solving efficiently sparse linear systems on distributed memory systems, using Message Passing Interface (MPI) communication library, is also presented along with theoretical estimates on speedups and efficiency. The implementation and performance on a distributed memory MIMD machine, using Message Passing Interface (MPI) is also investigated. Applications on characteristic initial/boundary value problems in three dimensions are discussed and numerical results are given.