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Parallel solution of closely coupled systems
Author(s) -
Utku S.,
Salama M.
Publication year - 1986
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620231203
Subject(s) - cholesky decomposition , permutation (music) , computer science , parallel computing , equivalence (formal languages) , factoring , topology (electrical circuits) , mathematics , theoretical computer science , discrete mathematics , combinatorics , eigenvalues and eigenvectors , physics , finance , quantum mechanics , acoustics , economics
The odd—even permutation and associated unitary transformations for reordering the matrix coefficient A is employed as a means of breaking the strong seriality which is characteristic of closely coupled systems. The nested dissection technique is also reviewed, and the equivalence between reordering A and dissecting its network is established. The effect of transforming A with odd—even permutation on its topology and the topology of its Cholesky factors is discussed. This leads to the construction of directed graphs showing the computational steps required for factoring A , their precedence relationships and their sequential and concurrent assignment to the available processors. Expressions for the speed‐up and efficiency of using N processors in parallel relative to the sequential use of a single processor are derived from the directed graph. Similar expressions are also derived when the number of available processors is fewer than required.