Title: Speedup in solving differential equations on clusters of workstations

Authors: Dana Petcu

Addresses: Department of Computer Science, Western University of Timisoara and Institute e-Austria Timisoara, B-dul V.Parvan 4, 300223 Timisoara, Romania

Abstract: A performance model is constructed for parallel iterative numerical methods under the assumption of a message-passing computing system. Arguments are given for the fact that the speedup of parallel iterative methods is mainly influenced by the speedup at one iterative step including computations and communications. Using the theoretical model, it is proved why explicit iterative methods for ordinary differential equations are inefficient in implementation on distributed memory multiprocessor systems. Numerical tests on a cluster of dedicated machines confirm the correctness of the theoretical model at least in the case of iterative methods for ordinary differential equations and time-dependent partial differential equations.

Keywords: performance modelling; cluster computing; problem solving environments; ordinary differential equations; partial differential equations; parallel iterative methods; parallel computing; message-passing computing.

DOI: 10.1504/IJCSE.2005.009698

International Journal of Computational Science and Engineering, 2005 Vol.1 No.2/3/4, pp.134 - 141

Published online: 05 May 2006 *

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