Research project "ELPA-AEO - Eigenvalue solvers for petaflop applications: algorithmic extensions and optimizations"

(Hochskalierbare Eigenwert-Löser für PetaFlop-Anwendungen: Algorithmische Erweiterungen und Optimierungen)

Researchers

Martin Galgon
Bruno Lang
Valeriy Manin
Lukas van Gemmeren

Duration and funding

Since February 2016.

From Feb 2016 to Jan 2019 this research was funded by Bundesministerium für Bildung und Forschung.

Description

The ELPA-AEO project extends the earlier ELPA project that provided efficient highly parallel routines for solving the generalized eigenproblems A x = B x λ occuring in, e.g., ab initio electronic structure computations. While the focus remained on this application area, the techniques and routines developed in the ELPA-AEO project were aimed at extending the range of applicability and improve the efficiency w.r.t. time and efficiency. This includes

efficient reduction of the generalized eigenproblem to a standard problem C z = z λ for band-structured matrices,
methods for "nearly banded" structures,
an iterative eigensolver,
adaptivity and auto-tuning to relieve the user from finding good parameter settings or algorithmic variants,
optimizations for current and emerging architectures.

The Wuppertal group mainly focused on algorithmic issues, including

improving the base algorithm for the reduction generalized-to-standard,
highly efficient parallel matrix multiplication if one of the factors is triangular,
multi-level parallel reduction of bandwidth (and corresponding back-transformation of eigenvectors).

The research on highly efficient direct eigensolvers is continued. Currently our investigations focus on techniques for

sequences of eigenproblems and
matrix multiplication.

Project-related publications

[1]	Valeriy Manin and Bruno Lang. Efficient parallel reduction of bandwidth for symmetric matrices. Parallel Comput., 115:102998:1--10, 2023. [ DOI \| Abstract ]
[2]	Valeriy Manin and Bruno Lang. Cannon-type triangular matrix multiplication for the reduction of generalized HPD eigenproblems to standard form. Parallel Comput., 91:102597:1--102597:14, March 2020. [ DOI \| Abstract ]
[3]	Hans-Joachim Bungartz, Christian Carbogno, Martin Galgon, Thomas Huckle, Simone Köcher, Hagen-Henrik Kowalski, Pavel Kus, Bruno Lang, Hermann Lederer, Valeriy Manin, Andreas Marek, Karsten Reuter, Michael Rippl, Matthias Scheffler, and Christoph Scheurer. ELPA: A parallel solver for the generalized eigenvalue problem. In Ian Foster, Gerard R. Joubert, Luděk Kučera, Wolfgang E. Nagel, and Frans Peters, editors, Parallel Computing: Technology Trends (Proc. ParCo2019, September 10--13, Prague), volume 36 of Advances in Parallel Computing, pages 647--668. IOS Press, Amsterdam, 2020. [ DOI \| Abstract ]
[4]	Michael Rippl, Bruno Lang, and Thomas Huckle. Parallel eigenvalue computation for banded generalized eigenvalue problems. Parallel Comput., 88:102542, October 2019. [ DOI \| Abstract ]
[5]	Andreas Alvermann, Achim Basermann, Hans-Joachim Bungartz, Christian Carbogno, Dominik Ernst, Holger Fehske, Yasunori Futamura, Martin Galgon, Georg Hager, Sarah Huber, Thomas Huckle, Akihiro Ida, Akira Imakura, Masatoshi Kawai, Simone Köcher, Moritz Kreutzer, Pavel Kus, Bruno Lang, Hermann Lederer, Valeriy Manin, Andreas Marek, Kengo Nakajima, Lydia Nemec, Karsten Reuter, Michael Rippl, Melven Röhrig-Zöllner, Tetsuya Sakurai, Matthias Scheffler, Christoph Scheurer, Faisal Shahzad, Danilo Simoes Brambila, Jonas Thies, and Gerhard Wellein. Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects. Japan J. Indust. Appl. Math., 36(2):699--717, 2019. [ DOI \| Abstract ]
[6]	Bruno Lang. Efficient reduction of banded hermitian positive definite generalized eigenvalue problems to banded standard eigenvalue problems. SIAM J. Sci. Comput., 41(1):C52--C72, 2019. [ DOI \| Abstract ]

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