Parallel solution of sparse algebraic equations

Journal Article · Sun May 01 00:00:00 EDT 1994 · IEEE Transactions on Power Systems (Institute of Electrical and Electronics Engineers); (United States)

OSTI ID:7154349

Lin, S L ^[1]; Ness, J.E. Van ^[2]

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1. Feng Chia Univ., Taichung (Taiwan, Province of China)
2. Northwestern Univ., Evanston, IL (United States)

Two methods that have been studied in recent years for solving large, sparse sets of algebraic equations, the multiple factoring method and the W-matrix method, are shown to be two independent methods of explaining equivalent computational procedures. The forward and backward substitution part of these methods are investigated using parallel processing techniques on commercially available computers. The results are presented from testing the proposed methods on two local memory machines, the Intel iPSC/1 and iPSC/860 hypercubes, and a shared memory machine, the Sequent SymmetryS81. With the iPSC/1, which is characterized by its slow communication rate and high communication overhead for a short message, the best speedup obtained is less than 2.5, and that was with only 8 of the 16 available processors in use. The iPSC/860, a more advance model of the iPSC family, is even worse as far as these parallel methods are concerned. Much better results were obtained on the Sequent Symmetry where a speedup of 7.48 was obtained with 16 processors.

• OSTI ID: 7154349
• Journal Information: IEEE Transactions on Power Systems (Institute of Electrical and Electronics Engineers); (United States), Journal Name: IEEE Transactions on Power Systems (Institute of Electrical and Electronics Engineers); (United States) Vol. 9:2; ISSN ITPSEG; ISSN 0885-8950
• Country of Publication: United States
• Language: English

Related Subjects

24 POWER TRANSMISSION AND DISTRIBUTION
240100* -- Power Systems-- (1990-)
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGEBRA
AUGMENTATION
COMPUTERS
DATA PROCESSING
EQUATIONS
HYPERCUBE COMPUTERS
MATHEMATICS
MEMORY DEVICES
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
PARALLEL PROCESSING
PROCESSING
PROGRAMMING
TASK SCHEDULING