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Modeling round-off errors in hydrodynamic simulations

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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https://hal.inria.fr/hal-03351754
Contributor : Louise Ben Salem-Knapp Connect in order to contact the contributor
Submitted on : Wednesday, September 22, 2021 - 3:15:43 PM
Last modification on : Friday, August 5, 2022 - 2:58:08 PM
Long-term archiving on: : Thursday, December 23, 2021 - 6:52:57 PM

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  • HAL Id : hal-03351754, version 1

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William Weens, Thibaud Vazquez-Gonzalez, Louise Ben Salem-Knapp. Modeling round-off errors in hydrodynamic simulations. NSV 2021 - 14th International Workshop on Numerical Software Verification, Jul 2021, Los Angeles, United States. ⟨hal-03351754⟩

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