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

Lossy data compression reduces communication time in hybrid time-parallel integrators 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. 1 Introduction As after N steps the exact solution has been computed, both in sequential and in parareal schemes, the parallel effi- Nowadays, the computing speed of single CPU cores barely ciency is bounded by 1/J , the inverse of the number of increases, such that performance gains are mostly due to iterations needed. A fast convergence within a small num- increasing parallelism: number of compute nodes, number ber of iterations independent of N usually requires http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computing and Visualization in Science Springer Journals

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

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Computer Applications in Chemistry; Algorithms; Visualization; Numerical Analysis; Calculus of Variations and Optimal Control; Optimization
ISSN
1432-9360
eISSN
1433-0369
D.O.I.
10.1007/s00791-018-0293-2
Publisher site
See Article on Publisher Site

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. 1 Introduction As after N steps the exact solution has been computed, both in sequential and in parareal schemes, the parallel effi- Nowadays, the computing speed of single CPU cores barely ciency is bounded by 1/J , the inverse of the number of increases, such that performance gains are mostly due to iterations needed. A fast convergence within a small num- increasing parallelism: number of compute nodes, number ber of iterations independent of N usually requires

Journal

Computing and Visualization in ScienceSpringer Journals

Published: May 29, 2018

References

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