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

  • Lisa Fischer
  • Sebastian Götschel
  • Martin Weiser
Special Issue Parallel-in-Time Methods
  • 71 Downloads

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.

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Lisa Fischer
    • 1
  • Sebastian Götschel
    • 1
  • Martin Weiser
    • 1
  1. 1.Zuse Institute BerlinBerlinGermany

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