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Title: The efficient parallel iterative solution of large sparse linear systems

Abstract

The development of efficient, general-purpose software for the iterative solution of sparse linear systems on a parallel MIMD computer requires an interesting combination of expertise. Parallel graph heuristics, convergence analysis, and basic linear algebra implementation issues must all be considered. In this paper, we discuss how we have incorporated recent results in these areas into a general-purpose iterative solver. First, we consider two recently developed parallel graph coloring heuristics. We show how the method proposed by Luby, based on determining maximal independent sets, can be modified to run in an asynchronous manner and give aa expected running time bound for this modified heuristic. In addition, a number of graph reduction heuristics are described that are used in our implementation to improve the individual processor performance. The effect of these various graph reductions on the solution of sparse triangular systems is categorized. Finally, we discuss the performance of this solver from the perspective of two large-scale applications: a piezoelectric crystal finite-element modeling problem, and a nonlinear optimization problem to determine the minimum energy configuration of a three-dimensional, layered superconductor model.

Authors:
;
Publication Date:
Research Org.:
Argonne National Lab., IL (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
10169715
Report Number(s):
ANL/CP-76726; CONF-9110404-1
ON: DE92018769
DOE Contract Number:  
W-31109-ENG-38
Resource Type:
Conference
Resource Relation:
Conference: IMA workshop on sparse matrix computations: graph theory issues and algorithms,Minneapolis, MN (United States),14-18 Oct 1991; Other Information: PBD: Jun 1992
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MATRICES; ITERATIVE METHODS; PARALLEL PROCESSING; ARRAY PROCESSORS; NONLINEAR PROBLEMS; SUPERCONDUCTIVITY; ALGORITHMS; 990200; MATHEMATICS AND COMPUTERS

Citation Formats

Jones, M T, and Plassmann, P E. The efficient parallel iterative solution of large sparse linear systems. United States: N. p., 1992. Web.
Jones, M T, & Plassmann, P E. The efficient parallel iterative solution of large sparse linear systems. United States.
Jones, M T, and Plassmann, P E. 1992. "The efficient parallel iterative solution of large sparse linear systems". United States. https://www.osti.gov/servlets/purl/10169715.
@article{osti_10169715,
title = {The efficient parallel iterative solution of large sparse linear systems},
author = {Jones, M T and Plassmann, P E},
abstractNote = {The development of efficient, general-purpose software for the iterative solution of sparse linear systems on a parallel MIMD computer requires an interesting combination of expertise. Parallel graph heuristics, convergence analysis, and basic linear algebra implementation issues must all be considered. In this paper, we discuss how we have incorporated recent results in these areas into a general-purpose iterative solver. First, we consider two recently developed parallel graph coloring heuristics. We show how the method proposed by Luby, based on determining maximal independent sets, can be modified to run in an asynchronous manner and give aa expected running time bound for this modified heuristic. In addition, a number of graph reduction heuristics are described that are used in our implementation to improve the individual processor performance. The effect of these various graph reductions on the solution of sparse triangular systems is categorized. Finally, we discuss the performance of this solver from the perspective of two large-scale applications: a piezoelectric crystal finite-element modeling problem, and a nonlinear optimization problem to determine the minimum energy configuration of a three-dimensional, layered superconductor model.},
doi = {},
url = {https://www.osti.gov/biblio/10169715}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jun 01 00:00:00 EDT 1992},
month = {Mon Jun 01 00:00:00 EDT 1992}
}

Conference:
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