Optimizing tridiagonal solvers for alternating direction methods on Boolean cube multiprocessors

Journal Article · Tue May 01 04:00:00 EDT 1990 · SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (USA)

DOI:https://doi.org/10.1137/0911032· OSTI ID:6411089

Ho, C T ^[1]; Johnsson, S L ^[2]

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1. IBM Almaden Research Center, San Jose, CA (US)
2. Dept. of Computer Science and Electrical Engineering, Yale Univ., New Haven, CT (US)

Sets of tridiagonal systems occur in many applications. Fast Poisson solvers and Alternate Direction Methods make use of tridiagonal system solvers. Network-based multiprocessors provide a cost-effective alternative to traditional supercomputer architectures. The complexity of concurrent algorithms for the solution of multiple tridiagonal systems on Boolean-cube-configured multiprocessors with distributed memory are investigated. Variations of odd-even cyclic reduction, parallel cyclic reduction, and algorithms making use of data transposition with or without substructuring and local elimination, or pipelined elimination, are considered. A simple performance model is used for algorithm comparison, and the validity of the model is verified on an Intel iPSC/1. For many combinations of machine and system parameters, pipelined elimination, or equation transposition with or without substructuring is optimum. Hybrid algorithms that at any stage choose the best algorithm among the considered ones for the remainder of the problem are presented. It is shown that the optimum partitioning of a set of independent tridiagonal systems among a set of processors yields the embarrassingly parallel case.

• OSTI ID: 6411089
• Journal Information: SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (USA), Journal Name: SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (USA) Vol. 11:3; ISSN 0196-5204; ISSN SIJCD
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
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HYPERCUBE COMPUTERS
PARALLEL PROCESSING
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