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 Acknowledgement
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 Abstract
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Title: On the LU factorization of sequences of identically structured sparse matrices within a distributed memory environment
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Permanent Link: http://ufdc.ufl.edu/UF00101365/00001
 Material Information
Title: On the LU factorization of sequences of identically structured sparse matrices within a distributed memory environment
Physical Description: Book
Language: English
Creator: Hadfield, Steven Michael
Publisher: Department of Computer and Information Science and Engineering, University of Florida
Place of Publication: Gainesville, Fla.
Copyright Date: 1991
 Subjects
Subjects / Keywords: Computer and Information Sciences thesis Ph.D
Parallel processing (Electronic computers)   ( lcsh )
Dissertations, Academic -- UF -- Computer and Information Sciences
Sparse matrices -- Data processing   ( lcsh )
Genre: bibliography   ( marcgt )
theses   ( marcgt )
 Notes
Abstract: This research effort studies the parallel LU factorization of sequences of identically structured sparse matrices using the unsymmetric pattern, multifrontal method of Davis and Duff. Computational burden is reduced by using the computational structure (called an assembly directed acyclic graph: DAG) that results from analysis of the first matrix for the numerical factorization of the subsequent matrices. Execution time is reduced via exploitation of parallelism in the assembly DAG. The theoretical parallelism in the assembly DAG is investigated using both analysis and simulation. Achievable parallelism is evaluated using a simulation model based on the nCUBE distributed memory multiprocessor. A fixed pivot order parallel LU factorization routine is implemented on the nCUBE and evaluated. Key subissues within this implementation are task scheduling, subcube allocation, subcube assignment, and data assignments to reduce communications and overall execution time. The resulting implementation is shown to be competitive with conventional techniques and demonstrates significant parallel performance with excellent scalability. Of greatest significance is the theoretical development and implementation of a lost pivot recovery capability for the unsymmetric patter, multifrontal method. The capability incorporates a lost pivot avoidance strategy with both inter- and intra- frontal matrix pivot recovery mechanisms. The inter-frontal matrix pivot recovery mechanisms migrate lost pivots to subsequent frontal matrices and accommodate corresponding side effects using relationships represented in the assembly DAG. Intra-frontal matrix pivot recoveries are done via a pipelined partial dense factorization kernel that handles unsymmetric permutations across processors. Evaluation of the lost pivot recovery capability using three matrix sequences from chemical engineering problems shows that significant execution time savings are afforded when executing on either a single processor or multiple processors.
General Note: Typescript.
General Note: Vita.
Thesis: Thesis (Ph. D.)--University of Florida, 1994.
Bibliography: Includes bibliographical references (leaves 360-371).
 Record Information
Bibliographic ID: UF00101365
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 001972742

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Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
        Page v
        Page vi
        Page vii
        Page viii
        Page ix
        Page x
        Page xi
    Abstract
        Page xii
        Page xiii
    Main
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