Computer Amdahl

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. 

Amdahl, G. M. Validity of the single processor approach to achieve large scale computing capabilities. In Proc. AFIPS spring computer conf. vol. 30. AFIPS Press, Reston, Virginia, 1967. 

An important aspect of an efficient implementation of any program on current and future high-performance computers is the level of parallelism. Our tests show that for the ZUj4 cluster 96% of the code is parallel and for larger clusters this ratio increases. Taking into account Amdahl s law (48) we can expect a factor of at least 3.5 improvement in performance (total time) on a four procesor machine. In the last column of Table VI the expected wall clock time is presented. 

Figure 7 shows how the HF application scales, based on this modified definition of Amdahl s law. The cases in Figure 7 are defined as parallel) overhead) The base case is (30,3000,30). Larger cases scale as 0 N), 0(N ), 0(N), respectively, which is similar to a traditional HF algorithm. For small problems, the serial and overhead terms are relatively important and become more so as the processor count increases. For the smallest case shown, overhead increases until it outweighs the actual computation, and the speed-up curve turns over, with the result that using more processors actually makes the computation go slower. Conversely, as the problem size is increased, the serial and overhead terms become less significant, and speed-up approaches the ideal linear curve. 

G. Amdahl, AFIPS, Comput. Conf., 30, 483 (1967). The Validity of the Single Processor Approach to Achieving Large Scale Computing Capabilities. 

To illustrate the characteristics of the combination of these three calculational procedures, Example 2-7 was selected. The statement of this example is presented in Table 2-2. The temperature profiles obtained by use of the Kb method on the basis of the corrected compositions found by use of the 6 method [Eqs. (2-27) and (2-28)] are presented in Table 2-3. The constants a and b in the expression for Kb [Eq. (2-31)] were found by use of the K values for /-C4H10 at 510 and 960°R. The values of 0 and the calculated values of D at the end of each trial are also listed in this table. The vapor rates computed by use of the constant-composition method, the temperatures found by the Kp method, and the corrected compositions are presented in Table 2-4. The solution sets d, and bi are presented in Table 2-5. To satisfy the convergence criterion, twelve trials were required and 2.60 seconds of computer time on an AMDAHL 470 V/6 computer using a WATFIV compiler. 

The convergence criteria were satisfied at the end of the 12th trial and 2.81 seconds on an AMDAHL 470 V/6 computer with the WATF1V compiler. 

Example Execution times and number of trials on an AMDAHL 470V/6 computer ... 

Example 7-4 Instead of specifying Lx and D for Example 2-7, modify this example by taking the two additional specifications to be the reflux ratio Ll/D = 2.0 and the boilup ratio VN/B= 1.80585. When these particular values for the reflux ratio and the boilup ratio are selected, the corresponding final solution is the same as the one shown in Tables 2-3 through 2-5. For this pair of additional specifications, nine iterations were required and 1.26 seconds of computer time (AMDAHL 470 V/6 computer, FORTRAN H EXTENDED). The convergence characteristics exhibited by this example for this version of the 0 method are shown in Table 7-12. 

AMDAHL, Computer time =0.16 s, WATFIV Compiler t The temperature 239.71°F is the dew-point temperature of the distillate, and the corresponding bubble-point temperature of the distillate (in the liquid state) is 224.83°F. 

Fig. 3. Sketch of the hardware and software system used in the author s laboratory to investigate the electrode kinetics of electrochemical reactions. D.A.C are digital-to-analogue convertors, F.R.A. is a frequency response analyser, A.D.C. are analogue-to-digital convertors (used to switch devices), D.P.M is a panel meter, and NTWK is the university network serial connection to an Amdahl computer. The units I are the appropriate interfaces.

Theoretical studies on ion structures and spectra were carried out using initially the Amdahl 450-V7 and more recently the IBM 308ID computer of the Northeast Regional Data Center at the University of Florida, and a Digital Equipment Corp. VAX 11/780 minicomputer in the Quantum Theory Project at UF. 

For high performance, the computer architecture must be planned using the principles discussed previously and Amdahl s law. 

The aim of this paper is to establish a basis for faster numerical techniques in the field of Elastohydrodynamic Lubrication and some comparisons with other methods are shown In Table 2. The comparison of run times is based on a typical run time carried out using the method of Houpert and Hamrock [3] on the Amdahl 580 computer at Leeds University and data published in [3]. 

A solution of the now complete set of nonlinear equations was achieved by developing an iterative scheme based on the successive approximation of the function Q(x). The method was programmed in Fortran 77 on the Amdahl computer at Leeds University to give the following results. 

A solution was deemed Co have converged if two successive runs of the computer program produced results which differed by less Chan 1%. In general about sixteen runs of Che computer program, each of 1800 c.p.u. secs., on the Amdahl V7 computer at Leeds University were required before this criterion was reached. 

The results presented were calculated on the Amdahl 5860 digital computer at the University of Leeds. There are two parameters in the problem, the dimensionless fluid flow rate Q and the dimensionless plate speed U. Normally the normalised plate velocity (n.p.v.) was chosen to be 1.0 and the normalised fluid flow rate was varied. The exception to this was that when the pressure on the moving plate was calculated an n.p.v. of 0.0 was desired, as well as an n.p.v, of 1.0, for a fixed flow rate. 

By using the LSSD discipline, IBM could verify that its designs would be completely testable, and those tests could be created by a computer program. Other companies such as Sperry Univac, Amdahl, Hitachi, etc., had similar proprietary structured approaches. Most smaller, nonintegrated companies were not able to participate in structured DFT— that is, until nonproprietary industry standards came into play. 

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