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Parallel Treatment of Block Bi-Diagonal Matrics in the Solution of Ordinary Differentail Boundary Value Problems

Lookup NU author(s): Dr Kenneth Wright



Ignoring boundary conditions, a number of schemes such as multiple shooting give rise to systems of equations of block-bidiagonal form. With some preliminary transformation others, such as collocation, can be reduced to this form. An algorithm which reduces a block-bidiagonal system of size n*(n+1) to a system of size 1*2 blocks will be described. These equations can then be combined with theboundary conditions and the solution completed. The reduction uses ideas similar to ""recursive doubling"" and ""block-cyclic reduction"", but full row interchanges are included. The algorithm is designed to facilitate the use of parallel processes. The algorithm has been implemented on the 14-processor Encore Multimax shared-memory multiprocessor in Newcastle. Results will be described for different numbers of processors and the algorithm compared with other possibilities.

Publication metadata

Author(s): Wright K

Publication type: Report

Publication status: Published

Series Title: Computing Laboratory Technical Report Series

Year: 1991

Pages: 18

Print publication date: 01/11/1991

Source Publication Date: November 1991

Report Number: 350

Institution: Computing Laboratory, University of Newcastle upon Tyne

Place Published: Newcastle upon Tyne