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The Parareal in Time Algorithm Applied to the Kinetic Neutron Diffusion Equation

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Book cover Domain Decomposition Methods in Science and Engineering XXI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 98))

Abstract

The parareal in time algorithm is a time domain decomposition method for the approximation of transient problems. Its implementation in a parallel fashion allows for significant speed-ups in the computing time and opens the door to long time computations that involve accurate propagators. In this work, we first propose to overview the different strategies for the parallelization of the algorithm. We will then study the speed-up provided by parareal on a concrete example: the kinetic neutron diffusion equation in a nuclear reactor core. Implementations have been carried out with the MINOS solver, which is a tool developed at CEA in the framework of the APOLLO3Ⓡproject. As a conclusion, we will discuss the possibility of using neutron diffusion as a coarse propagator for neutron transport.

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Acknowledgements

This work was supported in part by the joint research program MANON between CEA-Saclay and University Pierre et Marie Curie-Paris 6.

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Authors and Affiliations

  1. C.E.A, CEA Saclay - DEN/DANS/DM2S/SERMA/LLPR, 91191, Gif-Sur-Yvette Cedex, France

    A.-M. Baudron, J.-J. Lautard & O. Mula

  2. LRC MANON, Laboratoire de Recherche Conventionnée, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL, Lyon, France

    A.-M. Baudron, J.-J. Lautard, Y. Maday & O. Mula

  3. UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France

    Y. Maday & O. Mula

  4. Institut Universitaire de France, Paris, France

    Y. Maday

  5. Division of Applied Maths, Brown University, Providence, RI, USA

    Y. Maday

Authors
  1. A.-M. Baudron
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  2. J.-J. Lautard
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  3. Y. Maday
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  4. O. Mula
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Corresponding author

Correspondence to O. Mula .

Editor information

Editors and Affiliations

  1. INRIA, Rennes, France

    Jocelyne Erhel

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Géometrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. INRIA, Rennes, France

    Géraldine Pichot

  5. Laboratoire LMNO, Université de Caen, Caen, France

    Taoufik Sassi

  6. New York University Courant Institute, New York, New York, USA

    Olof Widlund

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Baudron, AM., Lautard, JJ., Maday, Y., Mula, O. (2014). The Parareal in Time Algorithm Applied to the Kinetic Neutron Diffusion Equation. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_41

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