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Lossy data compression reduces communication time in hybrid time-parallel integrators

  • Special Issue Parallel-in-Time Methods
  • Published:
Computing and Visualization in Science

Abstract

Parallel-in-time methods for solving initial value problems are a means to increase the parallelism of numerical simulations. Hybrid parareal schemes interleaving the parallel-in-time iteration with an iterative solution of the individual time steps are among the most efficient methods for general nonlinear problems. Despite the hiding of communication time behind computation, communication has in certain situations a significant impact on the total runtime. Here we present strict, yet not sharp, error bounds for hybrid parareal methods with inexact communication due to lossy data compression, and derive theoretical estimates of the impact of compression on parallel efficiency of the algorithms. These and some computational experiments suggest that compression is a viable method to make hybrid parareal schemes robust with respect to low bandwidth setups.

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Acknowledgements

Partial funding by BMBF Project SOAK and DFG Project WE 2937/6-1 is gratefully acknowledged. The authors would also like to thank Th. Steinke, F. Wende, A. Kammeyer and the North-German Supercomputing Alliance (HLRN) for supporting the numerical experiments.

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Authors and Affiliations

  1. Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Lisa Fischer, Sebastian Götschel & Martin Weiser

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  1. Lisa Fischer
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  2. Sebastian Götschel
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  3. Martin Weiser
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Correspondence to Martin Weiser.

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Fischer, L., Götschel, S. & Weiser, M. Lossy data compression reduces communication time in hybrid time-parallel integrators. Comput. Visual Sci. 19, 19–30 (2018). https://doi.org/10.1007/s00791-018-0293-2

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  • DOI: https://doi.org/10.1007/s00791-018-0293-2

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