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Modeling Round-Off Errors in Hydrodynamic Simulations

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Software Verification (NSV 2021, VSTTE 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 13124))

Abstract

The growth of the computing capacities makes it possible to obtain more and more precise simulation results. These results are often calculated in binary64 with the idea that round-off errors are not significant. However, exascale is pushing back the known limits and the problems of accumulating round-off errors could come back and require increasing further the precision. But working with extended precision, regardless of the method used, has a significant cost in memory, computation time and energy and would not allow to use the full performance of HPC computers. It is therefore important to measure the robustness of the binary64 by anticipating the future computing resources in order to ensure its durability in numerical simulations. For this purpose, numerical experiments have been performed and are presented in this article. Those were performed with weak floats which were specifically designed to conduct an empirical study of round-off errors in hydrodynamic simulations and to build an error model that extracts the part due to round-off error in the results. This model confirms that errors remain dominated by the scheme errors in our numerical experiments.

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Notes

  1. 1.

    If several realizations of the same experiment under identical conditions give exactly identical results, then the experiment is said to be reproducible.

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Author information

Authors and Affiliations

  1. CEA DAM DIF, 91297, Arpajon Cedex, France

    William Weens, Thibaud Vazquez-Gonzalez & Louise Ben Salem-Knapp

  2. Université Paris-Saclay, CEA, Laboratoire en Informatique Haute Performance pour le Calcul et la simulation, 91680, Bruyères-le-Châtel, France

    William Weens

  3. Université Paris-Saclay, CNRS, ENS Paris-Saclay, Inria, Laboratoire Méthodes Formelles, 91190, Gif-sur-Yvette, France

    Louise Ben Salem-Knapp

Authors
  1. William Weens
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  2. Thibaud Vazquez-Gonzalez
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  3. Louise Ben Salem-Knapp
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Corresponding author

Correspondence to Louise Ben Salem-Knapp .

Editor information

Editors and Affiliations

  1. Graz University of Technology, Graz, Austria

    Roderick Bloem

  2. CISPA, Helmholtz Center for Information Security, Saarbrücken, Germany

    Rayna Dimitrova

  3. Massachusetts Institute of Technology, Cambridge, MA, USA

    Chuchu Fan

  4. Faculty of Informatics, Università della Svizzera italiana, Lugano, Switzerland

    Natasha Sharygina

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Weens, W., Vazquez-Gonzalez, T., Salem-Knapp, L.B. (2022). Modeling Round-Off Errors in Hydrodynamic Simulations. In: Bloem, R., Dimitrova, R., Fan, C., Sharygina, N. (eds) Software Verification. NSV VSTTE 2021 2021. Lecture Notes in Computer Science(), vol 13124. Springer, Cham. https://doi.org/10.1007/978-3-030-95561-8_11

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  • DOI: https://doi.org/10.1007/978-3-030-95561-8_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-95560-1

  • Online ISBN: 978-3-030-95561-8

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