Bergische Universität Wuppertal
Fakultät für Mathematik und Naturwissenschaften
Angewandte Informatik - Algorithmik

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Research projects "ESSEX" and "ESSEX II" - "Equipping Sparse Solvers for Exascale"


Researchers

Martin Galgon
Sarah Huber
Lukas Krämer
Bruno Lang

Duration and funding

January 2013 to December 2015 (ESSEX),
January 2016 to December 2018 (ESSEX II),

funded by within the German Priority Programme 1648 "Software for Exascale Computing"

Description

The aim of the ESSEX project is to develop programming concepts and numerical methods for the solution of large scale sparse eigenvalue problems. The choice of the considered algorithms (left picture below) is driven by applications from physics, and the exascale challenges of extreme parallelism, energy efficiency, and resiliency are addressed by coherent software design between the Building Blocks, Algorithms, and Applications layers (right picture). The first ESSEX project was a joint research effort of groups at the Universities of Erlangen-Nuremberg, Greifswald and Wuppertal, and DLR Köln. The current ESSEX II team also includes groups at the Universities of Tsukuba and Tokyo in Japan.

                 

The work of the Wuppertal group originally was based on the FEAST algorithm for computing a bulk of eigenvalues in the interior of the spectrum. This algorithm has been introduced in [E. Polizzi: Density-matrix-based algorithm for solving eigenvalue problems. Phys. Rev. B 79:115112 (2009)]. In each iteration of the algorithm, a contour integral is used to approximately project the current "search space" onto the desired eigenspace, and a Rayleigh-Ritz type method is used to extract eigenvalue and eigenvector approximations from the resulting subspace.

Our research so far included work on

We have provided a scalable parallel implementation based on the highly optimized building blocks that are developed within the ESSEX project, and applied it to research problems from quantum physics.

Currently our research focuses on

Project-related publications

[1] 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, and Jonas Thies. Improved coefficients for polynomial filtering in ESSEX. In Tetsuya Sakurai, Shao-Liang Zhang, Toshiyuki Imamura, Yusaku Yamamoto, Yoshinobu Kuramashi, and Takeo Hoshi, editors, Eigenvalue Problems: Algorithms, Software and Applications, in Petascale Computing. Proc. EPASA 2015, Tsukuba, Japan, September 2015, volume 117 of LNCSE. Springer International Publishing, 2017. To appear. [ Abstract ]
[2] Moritz Kreutzer, Jonas Thies, Melven Röhrig-Zöllner, Andreas Pieper, Faisal Shahzad, Martin Galgon, Achim Basermann, Holger Fehske, Georg Hager, and Gerhard Wellein. GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems. Int. J. Parallel Prog., October 2016. [ http | Abstract ]
[3] Lukas Krämer and Bruno Lang. Convergence of integration based methods for the solution of standard and generalized hermitian eigenvalue problems. Preprint BUW-IMACM 14/30, 2016. [ .pdf | Abstract ]
[4] Andreas Pieper, Moritz Kreutzer, Andreas Alvermann, Martin Galgon, Holger Fehske, Georg Hager, Bruno Lang, and Gerhard Wellein. High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations. J. Comput. Phys., 325:226--243, 2016. [ http | Abstract ]
[5] Moritz Kreutzer, Jonas Thies, Andreas Pieper, Andreas Alvermann, Martin Galgon, Melven Röhrig-Zöllner, Faisal Shahzad, Achim Basermann, Alan R. Bishop, Holger Fehske, Georg Hager, Bruno Lang, and Gerhard Wellein. Performance engineering and energy efficiency of building blocks for large, sparse eigenvalue computations on heterogeneous supercomputers. In Hans-Joachim Bungartz, Philipp Neumann, and Wolfgang E. Nagel, editors, Software for Exascale Computing -- SPPEXA 2013--2015, volume 113 of LNCSE, pages 317--338. Springer, Switzerland, 2016. [ Abstract ]
[6] Jonas Thies, Martin Galgon, Faisal Shahzad, Andreas Alvermann, Moritz Kreutzer, Andreas Pieper, Melven Röhrig-Zöllner, Achim Basermann, Holger Fehske, Georg Hager, Bruno Lang, and Gerhard Wellein. Towards an exascale enabled sparse solver repository. In Hans-Joachim Bungartz, Philipp Neumann, and Wolfgang E. Nagel, editors, Software for Exascale Computing -- SPPEXA 2013--2015, volume 113 of LNCSE, pages 295--316. Springer, Switzerland, 2016. [ Abstract ]
[7] Martin Galgon, Lukas Krämer, and Bruno Lang. Adaptive choice of projectors in projection based eigensolvers. Preprint BUW-IMACM 15/07, 2015. [ .pdf | Abstract ]
[8] Martin Galgon, Lukas Krämer, Jonas Thies, Achim Basermann, and Bruno Lang. On the parallel iterative solution of linear systems arising in the FEAST algorithm for computing inner eigenvalues. Parallel Comput., 49:153--163, 2015. [ Abstract ]
[9] Martin Galgon, Lukas Krämer, Bruno Lang, Andreas Alvermann, Holger Fehske, and Andreas Pieper. Improving robustness of the FEAST algorithm and solving eigenvalue problems from graphene nanoribbons. Proc. Appl. Math. Mech., 14(1):821--822, December 2014. [ Abstract ]
[10] Andreas Alvermann, Achim Basermann, Holger Fehske, Martin Galgon, Georg Hager, Moritz Kreutzer, Lukas Krämer, Bruno Lang, Andreas Pieper, Melven Röhrig-Zöllner, Faisal Shahzad, Jonas Thies, and Gerhard Wellein. ESSEX: Equipping sparse solvers for exascale. In Luís Lopes et al., editors, Euro-Par 2014: Parallel Processing Workshops, volume 8806 of LNCS, pages 577--588. Springer, 2014. [ Abstract ]

Project-related theses

[1] Daniel Nagel. Parallelisierung der Parameteroptimierung für einen projektionsbasierten Eigenlöser. B.Sc. thesis, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 2017. In German.
[2] Sebastian Zeh. Auswirkungen und Erkennen von Silent Data Corruption in Algorithmen der numerischen linearen Algebra. M.Sc. thesis, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 2015. In German.
[3] Lukas Krämer. Integration based solvers for standard and generalized Hermitian eigenvalue problems. Dissertation, Bergische Universität Wuppertal, Germany, April 2014.

See also

the ESSEX home page,

the home pages of the PIs and researchers in the ESSEX project,

and the eigenvalue-related work on the Reseach page



University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics and Computer Science
Applied Computer Science Group

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