Abstract
Solving initial value problems (IVP) for ordinary differential equations (ODE) has long been believed to be an inherently sequential procedure. But extrapolation methods for solving ODEs which provide solutions of high quality possess a large potential of parallelism. In this article, we present a parallel algorithm for extrapolation based on the explicit Richardson-Euler method. A detailed theoretical runtime analysis using appropriate primitives for communication considers exact runtime, overhead and speedup for a hypercube architecteure. Experiments on the Intel iPSC/860 shows the numerical evidence of the theoretically computed runtimes.
Both authors supported by DFG, SFB 124
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References
D.P. Bertsekas and J.N. Tsitsiklis. Parallel and Distributed Computing. Prentice Hall, New York, NY, 1988.
A. Bingert, A. Formella, A.M. Müller, and W.J. Paul. Isolating the Reasons for the Performance of Parallel Machines on Numerical Programs. In International Workshop on Automatic Distributed Memory Parallelization, Automatic Data Distribution and Automatic Parallel Performance Prediction, pages 34–64, 1993.
Z. Bozkus, S. Ranka, and G. Fox. Benchmarking the CM-5 Multicomputer. In IEEE Proceedings, 1992.
E.G. Coffman, M.R. Garey, and D.S. Johnson. An Application of Bin-Packing to Multiprocessor Scheduling. SIAM Journal of Computing, 7(1):1–17, 1978.
M.A. Franklin. Parallel Solution of Ordinary Differential Equations. IEEE Transactions on Computers, 27(5):413–420, 1978.
D. Hutchinson and B.M.S. Khalaf. Parallel Algorithms for Solving Initial Value Problems: Front Broadening and Embedded Parallelism. Parallel Computing, 17:957–968, 1991.
S.L. Johnsson and C.T. Ho. Optimum Broadcasting and Personalized Communication in Hypercubes. IEEE Transactions on Computers, 38(9):1249–1268, 1989.
T. Rauber and G. Rünger. Load Balancing for Extrapolation Methods on Distributed Memory Multiprocessors. In Proceedings of the PARLE'94, Athen, Greece, July 1994.
J. Stoer and R. Bulirsch. Introduction to Numerical Analysis Springer, New York, 1990.
P.B. Worland. Parallel Methods for the Numerical Solution of Ordinary Differential Equations. IEEE Transactions on Computers, 25(10):1045–1048, 1976.
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© 1994 Springer-Verlag Berlin Heidelberg
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Rauber, T., Rünger, G. (1994). Hypercube implementation and performance analysis for extrapolation methods. In: Buchberger, B., Volkert, J. (eds) Parallel Processing: CONPAR 94 — VAPP VI. VAPP CONPAR 1994 1994. Lecture Notes in Computer Science, vol 854. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58430-7_24
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DOI: https://doi.org/10.1007/3-540-58430-7_24
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