A parallel block cyclic reduction algorithm for the fast solution of elliptic equations

E. Gallopoulos; Y. Saad

doi:10.1007/3-540-18991-2_33

A parallel block cyclic reduction algorithm for the fast solution of elliptic equations

E. Gallopoulos, Y. Saad

Computer Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

This paper presents an adaptation of the Block Cyclic Reduction (BCR) algorithm for a multi-vector processor. The main bottleneck of BCR lies in the solution of linear systems whose coefficient matrix is the product of tridiagonal matrices. This bottleneck is handled by expressing the rational function corresponding to the inverse of this product as a sum of elementary fractions. As a result the solution of this system leads to parallel solutions of tridiagonal systems. Numerical experiments performed on an Alliant FX/8 are reported.

Original language	English (US)
Title of host publication	Supercomputing - 1st International Conference, Proceedings
Editors	Theodore S. Papatheodorou, Constantine D. Polychronopoulos, Elias N. Houstis
Publisher	Springer Verlag
Pages	563-575
Number of pages	13
ISBN (Print)	9783540189916
DOIs	https://doi.org/10.1007/3-540-18991-2_33
State	Published - 1988
Event	1st International Conference on Supercomputing, 1987 - Athens, Greece Duration: Jun 8 1987 → Jun 12 1987

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	297 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	1st International Conference on Supercomputing, 1987
Country/Territory	Greece
City	Athens
Period	6/8/87 → 6/12/87

Bibliographical note

Funding Information:
This work was supported by the National Science Foundation under Grants No. US NSF DCR84-10110 and US NSF DCR85-'09970, the US Department of Energy under Grant No. DOE DE-FG02-85ER25001, by the US Air Force under Contract AFSOR-85-0211, and the IBM donation.

Publisher Copyright:
© 1988, Springer-Verlag.

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Gallopoulos, E., & Saad, Y. (1988). A parallel block cyclic reduction algorithm for the fast solution of elliptic equations. In T. S. Papatheodorou, C. D. Polychronopoulos, & E. N. Houstis (Eds.), Supercomputing - 1st International Conference, Proceedings (pp. 563-575). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 297 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-18991-2_33

A parallel block cyclic reduction algorithm for the fast solution of elliptic equations. / Gallopoulos, E.; Saad, Y.
Supercomputing - 1st International Conference, Proceedings. ed. / Theodore S. Papatheodorou; Constantine D. Polychronopoulos; Elias N. Houstis. Springer Verlag, 1988. p. 563-575 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 297 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Gallopoulos, E & Saad, Y 1988, A parallel block cyclic reduction algorithm for the fast solution of elliptic equations. in TS Papatheodorou, CD Polychronopoulos & EN Houstis (eds), Supercomputing - 1st International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 297 LNCS, Springer Verlag, pp. 563-575, 1st International Conference on Supercomputing, 1987, Athens, Greece, 6/8/87. https://doi.org/10.1007/3-540-18991-2_33

Gallopoulos E, Saad Y. A parallel block cyclic reduction algorithm for the fast solution of elliptic equations. In Papatheodorou TS, Polychronopoulos CD, Houstis EN, editors, Supercomputing - 1st International Conference, Proceedings. Springer Verlag. 1988. p. 563-575. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-18991-2_33

Gallopoulos, E. ; Saad, Y. / A parallel block cyclic reduction algorithm for the fast solution of elliptic equations. Supercomputing - 1st International Conference, Proceedings. editor / Theodore S. Papatheodorou ; Constantine D. Polychronopoulos ; Elias N. Houstis. Springer Verlag, 1988. pp. 563-575 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "This paper presents an adaptation of the Block Cyclic Reduction (BCR) algorithm for a multi-vector processor. The main bottleneck of BCR lies in the solution of linear systems whose coefficient matrix is the product of tridiagonal matrices. This bottleneck is handled by expressing the rational function corresponding to the inverse of this product as a sum of elementary fractions. As a result the solution of this system leads to parallel solutions of tridiagonal systems. Numerical experiments performed on an Alliant FX/8 are reported.",

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A parallel block cyclic reduction algorithm for the fast solution of elliptic equations

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