Improved coefficients for polynomial filtering in ESSEX

Conference paper (2017)

Authors

Martin Galgon Bergische Universität Wuppertal
Lukas Krämer Bergische Universität Wuppertal
Achim Basermann Deutsches Zentrum für Luft- und Raumfahrt (DLR)
Melven Röhrig-Zöllner Deutsches Zentrum für Luft- und Raumfahrt (DLR)
J. Thies German Aerospace Center
Bruno Lang Bergische Universität Wuppertal
Andreas Alvermann Greifswald University
Holger Fehske Greifswald University
Andreas Pieper Greifswald University
Georg Hager Erlangen Regional Computing Center
Moritz Kreutzer Erlangen Regional Computing Center
Faisal Shahzad Erlangen Regional Computing Center
Gerhard Wellein Erlangen Regional Computing Center
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Published Date

2017

Language

English

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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.