| 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 $ Oleft({psqrt s} right) $ in 2D and O(ps) in 3D, asymptotically as n/s → ∞. In particular, speed-ups with respect to Newmark's method of $ Oleft({psqrt s} right) $ 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. |
