SPEEDUP

The speedup is relative to the reference trajectory, which takes 14 hours. 

Fig. 11. The Speedup of LN at increasing outer timesteps for BPTI (2712 variables), lysozyme (6090 variables), and a large water system (without nonbonded cutoffs 37179 variables). For lysozyme, the CPU distribution among the fast, medium, and slow forces is shown for LN 3, 24, and 48.

In addition, the non-bonded forces can be divided into several regions according to pair distances. The near region is normally more important than the distant region because the non-bonded forces decay with distance. Since most of the CPU time in a MD simulation is spent in the calculation of these non-bonded interactions, the separation in pair distance results in valuable speedups. Using a 3-fold distance split, the non-bonded forces are separated in 3 regions near, medium, and fax distance zones. Thus, the Liouville operator can be express as a sum of five terms... 

The Fourier sum, involving the three dimensional FFT, does not currently run efficiently on more than perhaps eight processors in a network-of-workstations environment. On a more tightly coupled machine such as the Cray T3D/T3E, we obtain reasonable efficiency on 16 processors, as shown in Fig. 5. Our initial production implementation was targeted for a small workstation cluster, so we only parallelized the real-space part, relegating the Fourier component to serial evaluation on the master processor. By Amdahl s principle, the 16% of the work attributable to the serially computed Fourier sum limits our potential speedup on 8 processors to 6.25, a number we are able to approach quite closely. 

The complexity analysis shows that the load is evenly balanced among processors and therefore we should expect speedup close to P and efficiency close to 100%. There are however few extra terms in the expression of the time complexity (first order terms in TV), that exist because of the need to compute the next available row in the force matrix. These row allocations can be computed ahead of time and this overhead can be minimized. This is done in the next algorithm. Note that, the communication complexity is the worst case for all interconnection topologies, since simple broadcast and gather on distributed memory parallel systems are assumed. 

The time complexity of this algorithm shows that the force computation does not involve any extra overheads and therefore, the speedup should be equal to P and efficiency 100% in theory. 

Table 1 describes the timing results (in seconds) for a system of 4000 atoms on 4, 8 and 16 nodes. The average CPU seconds for 10 time steps per processor is calculated. In the case of the force-stripped row and force-row interleaving algorithms the CPU time is reduced by half each time the number of processors is doubled. This indicates a perfect speedup and efficiency as described in Table 2. Tables 3, refibm table3 and 5 describe the timing results, speedups and efficiencies for larger systems. In particular. Table 4 shows the scaling in the CPU time with increase in the system size. These results are very close to predicted theoretical results.

Table 2. Speedup and Efficiency results for a system of 4000 atoms on 4, 8 and 16 processors...

Cryoelectronics. Operation of CMOS devices at lower temperatures offers several advantages and some disadvantages (53). Operation at Hquid nitrogen temperatures (77 K) has been shown to double the performance of CMOS logic circuits (54). In part, this is the result of the increase in electron and hole mobilities with lower temperatures. The mobiHty decreases at high fields as carrier speeds approach saturation. Velocity saturation is more important for cryoelectronics because saturation velocities increase by only 25% at 77 K but saturation occurs at much lower fields. Although speedup can... 

Characteristics ASPEN PLUS Chemcad II Desiga-II Hysim Pio-11 Oiiasilin Span SPEEDUP... 

Fig. 1. Amdahl s law. Speedup as a function of the percentage of the program that can be vectorized. Lower curve vector—scalar speedup = 10 upper curve...

The lawn-mowing analogy is also interesting in that up to a certain point there will be a linear speedup as mowers are added. This speedup occurs because the mowers do not interfere with each other s work and have efficient mechanisms for coordinating their efforts. The lawn-mowing problem exhibits very good data paraHeHsm. 

Speedup. The good performance merits discussioa. The ideal parallel computer has as many as an infinite number of processors, as much as... 

Assume that the motor is designed for an average speedup torque of 135% and TpQ of 220% (Figure 7.21). If the average load torque is assumed as 68%, the average accelerating torque, 7, available will be 67% on DOL starting, i.e. 

Wynn (1992, 1993) have presented sliort-eut studies of solids proeess flowslieet-ing. Custom-written software to solve the model equations has been used by a number of authors. It has also been proposed that symbolie manipulation paekages, like Mathematiea, ean be used to solve the population balanee equations as a stand-alone modelling environment or as a set of modules to be linked to a generie proeess simulation paekage sueh as SPEEDUP (Hounslow, 1989 Sheikh and Jones, 1996). 

The optimal eontrol profiles identified by the solution of the non-linear programme were used to simulate the network through rigorous distributed parameter models on SPEEDUP to obtain a detailed deseription of its... 

Barton, G.W. and Perkins, J.D., 1988. Experiences with SPEEDUP in the mineral processing industries. Chemical Engineering Research and Design, 66, 408. 

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