Parallel preconditioned conjugate gradient square method based on normalized approximate inverses

Issue title: International Symposium of Parallel and Distributed Computing & International Workshop on Algorithms, Models and Tools for Parallel Computing on Heterogenous Networks

Article type: Research Article

Authors: Gravvanis, George A. | Giannoutakis, Konstantinos M.

Affiliations: Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, GR 67100 Xanthi, Greece. E-mail: {ggravvan,kgiannou}@ee.duth.gr

Note: [] Corresponding author

Abstract: 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.

Keywords: Finite difference method, sparse linear systems, normalized approximate inverse matrix techniques, preconditioning, parallel preconditioned conjugate gradient methods, programming, parallel computations, distributed computations

Journal: Scientific Programming, vol. 13, no. 2, pp. 79-91, 2005