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A non-intrusive parallel-in-time adjoint solver with the XBraid library

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Computing and Visualization in Science

Abstract

In this paper, an adjoint solver for the multigrid-in-time software library XBraid is presented. XBraid provides a non-intrusive approach for simulating unsteady dynamics on multiple processors while parallelizing not only in space but also in the time domain (XBraid: Parallel multigrid in time, http://llnl.gov/casc/xbraid). It applies an iterative multigrid reduction in time algorithm to existing spatially parallel classical time propagators and computes the unsteady solution parallel in time. Techniques from Automatic Differentiation are used to develop a consistent discrete adjoint solver which provides sensitivity information of output quantities with respect to design parameter changes. The adjoint code runs backwards through the primal XBraid actions and accumulates gradient information parallel in time. It is highly non-intrusive as existing adjoint time propagators can easily be integrated through the adjoint interface. The adjoint code is validated on advection-dominated flow with periodic upstream boundary condition. It provides similar strong scaling results as the primal XBraid solver and offers great potential for speeding up the overall computational costs for sensitivity analysis using multiple processors.

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Notes

  1. In this work, the application of \(\Phi ^i_{\rho }\) represents the approximate inversion of an operator (implicit scheme), but in principle, explicit schemes may be considered as well.

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Acknowledgements

The authors thanks Max Sagebaum (SciComp, TU Kaiserslautern) and Johannes Lotz (STCE, RWTH Aachen University) who provided insight and expertise on the implementation of AD.

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Authors and Affiliations

  1. Chair for Scientific Computing, TU Kaiserslautern, Paul-Ehrlich-Straße 34 – 36, 67663, Kaiserslautern, Germany

    Stefanie Günther & Nicolas R. Gauger

  2. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-561, Livermore, CA, 94551, USA

    Jacob B. Schroder

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  1. Stefanie Günther
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  2. Nicolas R. Gauger
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Correspondence to Stefanie Günther.

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This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52–07NA27344, LLNL-JRNL-730159.

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Günther, S., Gauger, N.R. & Schroder, J.B. A non-intrusive parallel-in-time adjoint solver with the XBraid library. Comput. Visual Sci. 19, 85–95 (2018). https://doi.org/10.1007/s00791-018-0300-7

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