Abstract
We study the conjugate gradient method to solve large sparse linear systems with two ways of preconditioning: the polynomial and the ILU preconditionings. A parallel version is evaluated on the Connection Machine 2 (CM-2) with large sparse matrices. Results show that we must find a tradeoff between high performance (in terms of Mflops) and fast convergence. We first conclude that to find efficient methods on massively parallel computers, especially when irregular structures were used, parallelising usual algorithms is not always the most efficient way. Then, we introduce the new massively parallel hybrid polynomial-ILUTmp (l, ε, d) preconditioning for distributed memory machines using a data parallel programming model.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
S. Ashby. Polynomial Preconditioning for Conjugate Gradient Methods. PhD thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, 1304 W. Springfield Avenue Urbana, IL 61801, december 1987.
S. Petiton. Massively Parallel Sparse Matrix Computations, Tech. Report YALEU/DSC/RR-878, Dept. Computer Science, Yale University, 1992.
S. Petiton and C. Weill-Duflos Very Sparse Preconditioned Conjugate Gradient on Massively Parallel Architectures. Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, Dublin, 1991.
Y. Saad. Practical use of polynomial preconditionings for the conjugate gradient method. SIAM J. SCI. STAT. COMP., 6(4), October 1985.
Y. Saad. ILUT: a dual thresholdind ILU preconditioning technique. Tech. Report to appear, Dept Computer Science, University of Minnesota, 1992.
J. Saltz, S. Petiton, H. Berryman, and A. Rifkin. Performance effects of irregular communications patterns on massively parallel multiprocessors. Journal of Parallel and Distributed Computing, 8 (1991).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Petiton, S., Weill-Duflos, C. (1992). Massively parallel preconditioners for the sparse conjugate gradient method. In: Bougé, L., Cosnard, M., Robert, Y., Trystram, D. (eds) Parallel Processing: CONPAR 92—VAPP V. VAPP CONPAR 1992 1992. Lecture Notes in Computer Science, vol 634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55895-0_433
Download citation
DOI: https://doi.org/10.1007/3-540-55895-0_433
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55895-8
Online ISBN: 978-3-540-47306-0
eBook Packages: Springer Book Archive