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At Sandia National Laboratories, we are currently engaged in research involving massively-parallel processing. There is considerable skepticism regarding the viability of massive parallelism; the skepticism centers around Amdahl's law, an argument put forth by Gene Amdahl in 1967 [1] that even when the fraction of serial work in a given problem is small, say s, the maximum speedup obtainable from even an infinite 220-601 Exam number of parallel processors is only 1/s. We now have timing results for a 1024-processor system that demonstrate that the assumptions underlying Amdahl's 1967 argument are inappropriate for the current approach to massive ensemble parallelism. If N is the number of processors, s is the amount of time spent (by a serial processor) on serial parts of a program and p is the amount of time spent (by a serial processor) on parts of the program that can be done in parallel, then Amdahl's law says that speedup is given by The steepness of the 220-602 Exam graph near s = 0 (approximately - N2 ) implies that very few problems will experience even a 100-fold speedup. Yet for three very practical applications (s = 0.4 - 0.8 percent) used at Sandia, we have achieved the speedup factors on a 1024-processor hypercube which we believe are unprecedented [2]: 1021 for beam stress analysis using conjugate gradients, 1020 for baffled surface wave simulation using explicit finite differences, and 1016 for unstable fluid flow using flux-corrected transport. How can this be, when Amdahl's argument would predict otherwise? The expression and graph both contain the implicit assumption that p is independent of N, which is virtually never the N10-003 Exam case. One does not take a fixed-size problem and run it on various numbers of processors except when doing academic research; in practice, the problem size scales with the number of processors. When given a more powerful processor, the problem generally expands to make use of the increased facilities. Users have control over such things as grid resolution, number of timesteps, difference operator complexity, and other parameters that are usually adjusted to allow the program to be run in some desired amount of time. Hence, it may be most realistic to assume that run time, not problem size, is constant.