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Improved Coefficients for Polynomial Filtering in ESSEX

  • Martin Galgon
  • Lukas Krämer
  • Bruno Lang
  • Andreas Alvermann
  • Holger Fehske
  • Andreas Pieper
  • Georg Hager
  • Moritz Kreutzer
  • Faisal Shahzad
  • Gerhard Wellein
  • Achim Basermann
  • Melven Röhrig-Zöllner
  • Jonas Thies
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 117)

Abstract

The ESSEX project is an ongoing effort to provide exascale-enabled sparse eigensolvers, especially for quantum physics and related application areas. In this paper we first briefly summarize some key achievements that have been made within this project.

Then we focus on a projection-based eigensolver with polynomial approximation of the projector. This eigensolver can be used for computing hundreds of interior eigenvalues of large sparse matrices. We describe techniques that allow using lower-degree polynomials than possible with standard Chebyshev expansion of the window function and kernel smoothing. With these polynomials, the degree, and thus the number of matrix–vector multiplications, typically can be reduced by roughly one half, resulting in comparable savings in runtime.

Notes

Acknowledgements

This work was supported by the German Research Foundation (DFG) through the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA) under project ESSEX. The authors would like to thank the unknown referees for their helpful comments.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Martin Galgon
    • 1
  • Lukas Krämer
    • 1
  • Bruno Lang
    • 1
  • Andreas Alvermann
    • 2
  • Holger Fehske
    • 2
  • Andreas Pieper
    • 2
  • Georg Hager
    • 3
  • Moritz Kreutzer
    • 3
  • Faisal Shahzad
    • 3
  • Gerhard Wellein
    • 3
  • Achim Basermann
    • 4
  • Melven Röhrig-Zöllner
    • 4
  • Jonas Thies
    • 4
  1. 1.School of Mathematics and Natural SciencesUniversity of WuppertalWuppertalGermany
  2. 2.Institute of PhysicsUniversity of GreifswaldGreifswaldGermany
  3. 3.Erlangen Regional Computing CenterErlangenGermany
  4. 4.Simulation and Software TechnologyGerman Aerospace Center (DLR)CologneGermany

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