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Communications oriented programming of parallel iterative solutions of sparse linear systems. (English) Zbl 0634.65021

Computing systems of the future for large-scale scientific and engineering computations will consist of many processors and memories working in parallel to solve a single problem. Efficient use and ease of use of these future systems are two basic problems facing potential users. The development of new parallel algorithms and parallel programming environments is essential for progress toward the solution of these problems. In this paper we develop parallel algorithms for a class of scientific computational problems by partitioning the problems into smaller problems which may be solved concurrently. The effectiveness of the resulting parallel solutions are determined by the amount and frequency of communication and synchronization and the extent to which communication can be overlapped with computation. We present three different parallel algorithms for solving the same class of problems and analyze their effectiveness from this point of view. The algorithms are programmed using a new programming environment. Run-time statistics and experience obtained from the execution of these programs assist in measuring the effectiveness of these algorithms.

MSC:

65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
65Y05 Parallel numerical computation
68N25 Theory of operating systems
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References:

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