Parallel Computer Architectures

The observation that certain kinds of parallel-computing architectures best support only certain kinds of problems seems to be general. The further observation that interprocessor communication can be the primary impediment to parallel performance is also general. As of this writing, any hope of a truly general purpose parallel computer seems to be remote. The best hope may He in software efforts that describe problems at higher levels of abstraction, which can then be ported and optimized for different parallel architectures (22). 

Section II discusses the real wave packet propagation method we have found useful for the description of several three- and four-atom problems. As with many other wave packet or time-dependent quantum mechanical methods, as well as iterative diagonalization procedures for time-independent problems, repeated actions of a Hamiltonian matrix on a vector represent the major computational bottleneck of the method. Section III discusses relevant issues concerning the efficient numerical representation of the wave packet and the action of the Hamiltonian matrix on a vector in four-atom dynamics problems. Similar considerations apply to problems with fewer or more atoms. Problems involving four or more atoms can be computationally very taxing. Modern (parallel) computer architectures can be exploited to reduce the physical time to solution and Section IV discusses some parallel algorithms we have developed. Section V presents our concluding remarks. 

Hamiltonian hopping, as any other version of parallel tempering, is highly efficient if it is implemented on parallel computer architectures. In a stratified FEP calculation involving N states of the system, the simulations of the different A states are carried out in parallel on separate processors. After a predefined number of steps, A ampie, N/2 swaps between two randomly chosen simulation cells are attempted [38]. This procedure is illustrated in Fig. 2.11. Acceptance of the proposed exchange between cells i and j is ruled by the following probability [39] ... 

One needs to match formulations to the available technology parallel computing architectures give some algorithms a head start. 

With the advent of first principles computational methods, highly scalable software and parallel computer architectures, more elaborate and accurate classical force fields than those discussed in the preceding section are being developed for predictions of physical and chemical properties of energetic solids. As indicated in section 2 of this chapter there are several... 

Vivarelli et al. (1995) used a hybrid system that combined a local genetic algorithm (LGA) and neural networks for the protein secondary structure prediction. The LGA, a version of the genetic algorithms (GAs), was particularly suitable for parallel computational architectures. Although the LGA was effective in selecting different... 

Impressive work implementing and applying various coupled-cluster codes on parallel computer architectures was reported by Rendell and coworkers, Rendell, Lee, and Lindh presented a formulation of the singles... 

D. J. Kuck, E. S. Davidson, D. H. Lawrie, and A. H. Sameh, in Experimental Parallel Computing Architectures, J. Dongarra, Ed., Elsevier Science Publishers, Amsterdam, 1987, pp. 1-23. Parallel Supercomputing Today and the Cedar Approach. 

M. W. Feyereisen and R. A. Kendall, Theor. Chim. Acta, 84, 289 (1993). An Efficient Implementation of the Direct-SCF Algorithm on Parallel Computer Architectures. 

A. P. Rendell, T. J. Lee, and R. Lindh, Chem. Phys. Lett., 194, 84 (1992). Quantum Chemistry on Parallel Computer Architectures Coupled-Cluster Theory Applied to the Bending Potential of Fulminic Acid. 

The constant increase of computing power at a reasonable price allows now complex simulations of protein behaviour on massively parallel computing architecture. It will thus be conceivable to study the dynamic properties of supramolecular assemblies in the near future. 

Parallel computers are often classified according to a scheme proposed by Michael Flynn in 1972. In the Flynn taxonomy, illustrated in Table 2.1, there are four classes of parallel computers, distinguished on the basis of the flow of data and instructions an application running on a computer is viewed as one or more sequences (or "streams") of instructions and one or more streams of data, and computers are divided into four classes depending on whether multiple streams of data or instructions are permitted. Three of these four classes of parallel computer architectures are of interest for quantum chemistry applications and are discussed in detail next. 

This book is divided into two parts. In Part 1 we will discuss parallel computer architectures as well as parallel computing concepts and terminology with a focus on good parallel program design and performance... 

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