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CivilComp Proceedings
ISSN 17593433 CCP: 112
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GPU AND CLOUD COMPUTING FOR ENGINEERING Edited by: P. Iványi and B.H.V. Topping
Paper 17
Distributed asynchronous convergence detection without detection protocol G. GbikpiBenissan^{1} and F. Magoules^{2}
^{1}RUDN University, Russia
G. GbikpiBenissan, F. Magoules, "Distributed asynchronous convergence detection
without detection protocol", in P. Iványi, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Parallel, Distributed, GPU and Cloud Computing for Engineering", CivilComp Press, Stirlingshire, UK, Paper 17, 2019. doi:10.4203/ccp.112.17
Keywords: asynchronous iterations, convergence detection, global residual, parallel computing.
Summary
One of the major questions which arise when implementing asynchronous iterations consists
of finding a mechanism to detect when convergence is reached. On efficiency aspects,
centralized detection protocols suffer from scaling limits, and more elaborated mechanisms
may imply termination delays. On the other hand, effective convergence is hardly guaranteed
when resorting to assumptionsbased protocols. One thus has to figure out what is the most
appropriate choice according to his parallel configuration.
To be more precise, let a sequence of vectors be generated by asynchronous iterations to find the solution of a fixedpoint problem. In such a context, this sequence of vectors is actually implicit, and one only explicitly handles parallel sequences of local subvectors. The asynchronous convergence detection problem therefore consists of determining, in a nonblocking way, and as quickly as possible, the moment when a residual error evaluation function would nearly vanish if applied to a gathered potential solution. The main distributed approaches consist of: modifying the iterative procedure to ensure finitetime termination, explicitly evaluating residual errors from global state snapshots, approximating the number of iterations required to reach convergence, monitoring both the consistency and the persistence of local convergence, evaluating the diameter of solutions nested sets by means of “macroiterations”. Modifying the iterative procedure is intrusive and even requires additional assumptions over the asynchronous iterative model. Making use of nested sets was investigated only on mathematical aspects, and suggests the need of intrusive piggybacking techniques. The monitoringbased and the predictionbased approaches can lead to untimely termination, which requires a postdetection final check. The snapshot method introduces computation data into snapshot messages, which leads to an O(n) communication overhead. In our earlier work an O(1) snapshot message size is achieved, but at the cost of assuming a bound on communication delays. The analysis therein shows the evaluation of an approximated residual error, while this approximation is explicitly bounded. Roughly, it allows for a non consistent snapshot. We therefore investigate, in this paper, to which extent such a snapshot could be non consistent, which even allows us to consider no control at all, meaning not performing any prior snapshot protocol. We performed several experiments on a supercomputer, with up to 504 processor cores, for solving a convectiondiffusion equation in a regular 3D grid geometry, by means of an asynchronous iterative method based on a mixed Jacobi and GaussSeidel relaxation scheme. purchase the fulltext of this paper (price £22)
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