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Efficiency of group implicit concurrent algorithms for transient finite element analysis
Author(s) -
Ortiz M.,
Sotelino E. D.,
NourOmid B.
Publication year - 1989
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.1620281204
Subject(s) - computation , hypercube , partition (number theory) , finite element method , speedup , parallel computing , reduction (mathematics) , group (periodic table) , computer science , transient (computer programming) , element (criminal law) , algorithm , mathematics , combinatorics , physics , geometry , quantum mechanics , operating system , thermodynamics , political science , law
The performance of group implicit algorithms is assessed on actual concurrent computers. We show that, as the number of subdomains is increased, performance enhancements are derived from two sources: the increased parallelism in the computations; and a reduction in equation solving effort. Moreover, we show that these two performance enhancements are synergistic, in the sense that the corresponding speed‐ups are multiplied , rather than merely added . Our numerical simulations demonstrate that, if n is the number of degrees of freedom of the structure, p the number of processors used in the computations, and s ⩾ p is the number of subdomains in the partition, the net speed‐up is \documentclass{article}\pagestyle{empty}\begin{document}$ O\left({p\sqrt s} \right) $\end{document} in 2D and O ( ps ) in 3D, asymptotically as n / s → ∞. In particular, speed‐ups with respect to Newmark's method of \documentclass{article}\pagestyle{empty}\begin{document}$ O\left({p\sqrt s} \right) $\end{document} in 2D and O ( s ) in 3D are obtained on a single‐processor machine. Finally, simulations on a 32‐node hypercube are presented for which the interprocessor communication efficiencies obtained are consistently in excess of 90 per cent.