An Efficient Parallel Algorithm for the Solution of Block Tridiagonal Linear Systems

Takashi NARITOMI; Hirotomo ASO

An Efficient Parallel Algorithm for the Solution of Block Tridiagonal Linear Systems

Takashi NARITOMI, Hirotomo ASO

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A parallel overlapping preconditioner is applied to ICCG method and the effect of the parallel preconditioning on the convergence of the method is investigated by solving large scale block tridiagonal linear systems arising from the discretization of Poisson's equation. Compared with the original ICCG method, the parallel preconditioned ICCG method can solve the problems in high parallelism with slight increasing the number of iterations. Furthermore, the speedup and the efficiency are evaluated for the parallel preconditioned ICCG method by substituting the experimental results into formulae of complexity. For example, when a domain of simulation is discretized on a 250250 rectangular grid and the preconditioner is divided into 249 smaller ones, its speedup is 146.3 with the efficiency 0.59.

Publication: IEICE TRANSACTIONS on Information Vol.E78-D No.3 pp.256-262

Publication Date: 1995/03/25

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Type of Manuscript: PAPER

Category: Algorithm and Computational Complexity

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Takashi NARITOMI, Hirotomo ASO, "An Efficient Parallel Algorithm for the Solution of Block Tridiagonal Linear Systems" in IEICE TRANSACTIONS on Information, vol. E78-D, no. 3, pp. 256-262, March 1995, doi: .
Abstract: A parallel overlapping preconditioner is applied to ICCG method and the effect of the parallel preconditioning on the convergence of the method is investigated by solving large scale block tridiagonal linear systems arising from the discretization of Poisson's equation. Compared with the original ICCG method, the parallel preconditioned ICCG method can solve the problems in high parallelism with slight increasing the number of iterations. Furthermore, the speedup and the efficiency are evaluated for the parallel preconditioned ICCG method by substituting the experimental results into formulae of complexity. For example, when a domain of simulation is discretized on a 250250 rectangular grid and the preconditioner is divided into 249 smaller ones, its speedup is 146.3 with the efficiency 0.59.
URL: https://global.ieice.org/en_transactions/information/10.1587/e78-d_3_256/_p

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@ARTICLE{e78-d_3_256,
author={Takashi NARITOMI, Hirotomo ASO, },
journal={IEICE TRANSACTIONS on Information},
title={An Efficient Parallel Algorithm for the Solution of Block Tridiagonal Linear Systems},
year={1995},
volume={E78-D},
number={3},
pages={256-262},
abstract={A parallel overlapping preconditioner is applied to ICCG method and the effect of the parallel preconditioning on the convergence of the method is investigated by solving large scale block tridiagonal linear systems arising from the discretization of Poisson's equation. Compared with the original ICCG method, the parallel preconditioned ICCG method can solve the problems in high parallelism with slight increasing the number of iterations. Furthermore, the speedup and the efficiency are evaluated for the parallel preconditioned ICCG method by substituting the experimental results into formulae of complexity. For example, when a domain of simulation is discretized on a 250250 rectangular grid and the preconditioner is divided into 249 smaller ones, its speedup is 146.3 with the efficiency 0.59.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - An Efficient Parallel Algorithm for the Solution of Block Tridiagonal Linear Systems
T2 - IEICE TRANSACTIONS on Information
SP - 256
EP - 262
AU - Takashi NARITOMI
AU - Hirotomo ASO
PY - 1995
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E78-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 1995
AB - A parallel overlapping preconditioner is applied to ICCG method and the effect of the parallel preconditioning on the convergence of the method is investigated by solving large scale block tridiagonal linear systems arising from the discretization of Poisson's equation. Compared with the original ICCG method, the parallel preconditioned ICCG method can solve the problems in high parallelism with slight increasing the number of iterations. Furthermore, the speedup and the efficiency are evaluated for the parallel preconditioned ICCG method by substituting the experimental results into formulae of complexity. For example, when a domain of simulation is discretized on a 250250 rectangular grid and the preconditioner is divided into 249 smaller ones, its speedup is 146.3 with the efficiency 0.59.
ER -