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Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

  • Special Feature: Original Paper
  • International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2018)
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Abstract

We first briefly report on the status and recent achievements of the ELPA-AEO (Eigen value Solvers for Petaflop Applications—Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.

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Acknowledgements

The authors thank the unknown referees for their valuable comments that helped to improve and clarify the presentation.

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Authors and Affiliations

  1. Institute of Physics, University of Greifswald, Greifswald, Germany

    Andreas Alvermann & Holger Fehske

  2. German Aerospace Center (DLR), Cologne, Germany

    Achim Basermann, Melven Röhrig-Zöllner & Jonas Thies

  3. Department of Informatics, Technical University of Munich, Munich, Germany

    Hans-Joachim Bungartz, Thomas Huckle & Michael Rippl

  4. Fritz Haber Institute of the Max Planck Society, Berlin, Germany

    Christian Carbogno, Matthias Scheffler & Danilo Simoes Brambila

  5. High Performance Computing, University of Erlangen-Nuremberg, Erlangen, Germany

    Dominik Ernst, Georg Hager, Moritz Kreutzer, Faisal Shahzad & Gerhard Wellein

  6. Applied Mathematics, University of Tsukuba, Tsukuba, Japan

    Yasunori Futamura, Akira Imakura & Tetsuya Sakurai

  7. Mathematics and Natural Sciences, University of Wuppertal, Wuppertal, Germany

    Martin Galgon, Sarah Huber, Bruno Lang & Valeriy Manin

  8. Computer Science, The University of Tokyo, Tokyo, Japan

    Akihiro Ida, Masatoshi Kawai & Kengo Nakajima

  9. Department of Theoretical Chemistry, Technical University of Munich, Munich, Germany

    Simone Köcher, Lydia Nemec, Karsten Reuter & Christoph Scheurer

  10. Max Planck Computing and Data Facility, Garching, Germany

    Pavel Kus, Hermann Lederer & Andreas Marek

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  1. Andreas Alvermann
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  30. Faisal Shahzad
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Corresponding author

Correspondence to Bruno Lang.

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This work has been supported by the Deutsche Forschungsgemeinschaft through the priority programme 1648 “Software for Exascale Computing” (SPPEXA) under the project ESSEX-II and by the Federal Ministry of Education and Research through the project “Eigenvalue soLvers for Petaflop Applications—Algorithmic Extensions and Optimizations” (ELPA-AEO) under Grant No. 01H15001.

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Alvermann, A., Basermann, A., Bungartz, HJ. et al. Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects. Japan J. Indust. Appl. Math. 36, 699–717 (2019). https://doi.org/10.1007/s13160-019-00360-8

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  • DOI: https://doi.org/10.1007/s13160-019-00360-8

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