Efficiency of group implicit concurrent algorithms for transient finite element analysis
Miguel Ortiz, Elisa D. Sotelino, Bahram Nour‐Omid · International Journal for Numerical Methods in Engineering · 1989
Abstract 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.