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CivilComp Proceedings
ISSN 17593433 CCP: 90
PROCEEDINGS OF THE FIRST INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED AND GRID COMPUTING FOR ENGINEERING Edited by:
Paper 43
Performance Prediction for Multigrid Codes Implemented with Different Parallel Strategies G. Romanazzi^{1} and P.K. Jimack^{2}
^{1}CMUC, Department of Mathematics, University of Coimbra, Portugal
G. Romanazzi, P.K. Jimack, "Performance Prediction for Multigrid Codes Implemented with Different Parallel Strategies", in , (Editors), "Proceedings of the First International Conference on Parallel, Distributed and Grid Computing for Engineering", CivilComp Press, Stirlingshire, UK, Paper 43, 2009. doi:10.4203/ccp.90.43
Keywords: parallel distributed algorithms, performance evaluation and prediction, multigrid numerical software.
Summary
This paper investigates the modelling and prediction of the performance of
a class of parallel numerical multigrid software that can be implemented
with different geometric partitioning of the computational work across a
distributed memory architecture. A relatively simple empirical model is
proposed, with the goal of allowing reliable predictions to be made as to
the execution time of a given parallel code, on a large number of processors
of a given parallel system, by only benchmarking the code on small numbers
of processors.
When extra memory and processors are available, parallel multilevel
implementations are able to solve problems numerically on finer meshes,
so as to achieve greater accuracy than would be otherwise possible.
The methodology described permits us to estimate the performance prior
to actually running with these very fine meshes on large numbers of
processors. This is of great potential value in making decisions
concerning the choice of resources and the scheduling of jobs within a
multicluster or a Grid environment.
Following a short introduction, Section 2 of the paper describes some recent related work into performance modelling for parallel numerical software. In Section 3, we then provide a short summary of our previous work [1,2,3] in this area, where we have implemented predictive methodology for parallel multilevel software running across a onedimensional strip partition of data and processors. The methodology used in this prior work is exploited in this new research for modelling and predicting the performance of multigrid software with different partitioning strategies, such as using a twodimensional block partitioning approach for example. The parallel execution time is assumed to be representable as the sum of two terms: the core computational time (on the slowest processor) and the parallel overhead (the latter being primarily due to interprocessor communications). Section 4 of the paper describes the methodology used to model both the computational time and the parallel overhead. In order to predict the communications patterns for large parallel runs, we use only information based on the patterns observed for sequences of runs across small numbers of processors. Finally, in Section 5, a selection for numerical results obtained using our methodology are presented and discussed. We demonstrate that the approach is robust and accurate across different parallel architectures, sizes of problem and partitioning strategies used. References
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