Abstractions for Portable, Scalable Parallel Programming
IEEE Transactions on Parallel and Distributed Systems
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We analyze a problem in hydrodynamics from the standpoint of computation on a data flow compute that is not yet fully specified, with the objectives of helping to further specify the computer and helping to develop VAL as its source language. Lawrence Livermore Laboratory supplied the algorithm for hydrodynamics, including heat flow, as a 1749-line FORTRAN code called SIMPLE. The algorithm viewed as ''abstract'' (i.e. independent of physical arrangements in space and time for its realization) is shown to imply spatial and temporal structure that must appear in any and all implementations. Both for hardware design and program compilation it is useful to map this structure to grosser levels of description, with the grosser levels reflecting modularity of computational resources conjoined with modularity of the algorithm. Following Holt (1979) we use role diagrams to display spatio-temporal structure at different descriptive levels, so as to guide translation into VAL as well as the analysis of the time to compute. Inter-resource communication essential to the problem is displayed, and various issues of machine design are defined. Using VAL with one set of extensions, we express the algorithms so that in principle it can be compiled for execution by a data flow computer. Input-output functions beyond those implied by the SIMPLE code are discussed. A second set of extensions to VAL is advocated to express the conjunction of problem and resource modularity, so as to guide compilation. The dependence of time to compute on the number of processing units is shown for various aspects of the problem.