A Parallel Algorithm To Solve Large Stiff ODE Systems On Grid Systems

Authors:
Jacques M. Bahi;Jean-Claude Charr;Raphaël Couturier;David Laiymani
Affiliations:
AND TEAM (DISTRIBUTED NUMERICAL ALGORITHMICS TEAM),LABORATOIRE D'INFORMATIQUE DE L'UNIVERSITÉ DE FRANCHE-COMTÉ (LIFC), UNIVERSITY OF FRANCHE-COMTÉ, FRANCE;AND TEAM (DISTRIBUTED NUMERICAL ALGORITHMICS TEAM),LABORATOIRE D'INFORMATIQUE DE L'UNIVERSITÉ DE FRANCHE-COMTÉ (LIFC), UNIVERSITY OF FRANCHE-COMTÉ, FRANCE;AND TEAM (DISTRIBUTED NUMERICAL ALGORITHMICS TEAM),LABORATOIRE D'INFORMATIQUE DE L'UNIVERSITÉ DE FRANCHE-COMTÉ (LIFC), UNIVERSITY OF FRANCHE-COMTÉ, FRANCE;AND TEAM (DISTRIBUTED NUMERICAL ALGORITHMICS TEAM),LABORATOIRE D'INFORMATIQUE DE L'UNIVERSITÉ DE FRANCHE-COMTÉ (LIFC), UNIVERSITY OF FRANCHE-COMTÉ, FRANCE
Venue:
International Journal of High Performance Computing Applications
Year:
2009

Citing 10
Cited 0

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Abstract

This paper introduces a parallel algorithm to solve large stiff ODE systems on distributed clusters, with computing nodes geographically distant from each other. This algorithm is based on the waveform relaxation method coupled with a sequential solver for differential equations systems. With respect to the standard PVODE algorithm (Parallel Variable-coefficient Ordinary Differential Equations solver; Byrne, George, and Hindmars 1999), it drastically reduces the number of messages exchanged between nodes which makes it less sensitive to slow communications. Thus, it is a coarse-grained algorithm well suited for grid environments connected via high latency networks. In this paper, we present various experiments which compare the PVODE solver and our algorithm and which show the benefits brought by this work.