Research project "ELPA - Eigenvalue solvers for petaflop applications"

(Hochskalierbare Eigenwert-Löser für PetaFlop-Anwendungen)

Researchers

Andreas Frommer
Martin Galgon
Lukas Krämer
Bruno Lang
Paul Willems

Duration and funding

December 2008 to November 2011, funded by Bundesministerium für Bildung und Forschung

Description

In the ELPA project, groups facing eigenvalue problems in applications from electronic structure calculations to the analysis of technical and biological networks, and groups with expertise in numerical algorithms, parallelization, and performance optimization joined forces to develop and optimize algorithms for solving these eigenvalue problems on massively parallel systems. The Wuppertal group mainly focused on algorithmic issues, including

two-step reduction of full and banded matrices to tridiagonal form (and corresponding back transformation of the eigenvectors), for real and complex matrices,
a variant of the divide-and-conquer tridiagonal eigensolver with reduced complexity, if only a part of the eigensystem is required,
a completely reworked MR³ algorithm with improved robustness, allowing for different factorizations and representations,
a hybrid divide-and-conquer/MR³ approach,
improvements of the FEAST eigensolver toward making it a robust building block for an iterative "complete eigensystem" solver.

Project-related publications

[1]	A. Marek, V. Blum, R. Johanni, V. Havu, B. Lang, T. Auckenthaler, A. Heinecke, H.-J. Bungartz, and H. Lederer. The ELPA library: Scalable parallel eigenvalue solutions for electronic structure theory and computational science. J. Phys.: Condens. Matter, 26(21):213201, May 2014. [ DOI \| Abstract ]
[2]	Andreas Marek, Volker Blum, Rainer Johanni, Ville Havu, Bruno Lang, Thomas Auckenthaler, Alexander Heinecke, Hans-Joachim Bungartz, and Hermann Lederer. The ELPA library -- scalable parallel eigenvalue solutions for electronic structure theory and computational science. Scientific highlight of the month, Ψ_k (http://www.psi-k.net), December 2013. [ .pdf \| Abstract ]
[3]	Lukas Krämer, Edoardo Di Napoli, Martin Galgon, Bruno Lang, and Paolo Bientinesi. Dissecting the FEAST algorithm for generalized eigenproblems. J. Comput. Appl. Math., 244:1--9, May 2013. [ DOI \| Abstract ]
[4]	Paul R. Willems and Bruno Lang. A framework for the MR³ algorithm: Theory and implementation. SIAM J. Sci. Comput., 35(2):A740--A766, 2013. [ DOI \| Abstract ]
[5]	Paul R. Willems and Bruno Lang. The MR³-GK algorithm for the bidiagonal SVD. Electron. Trans. Numer. Anal., 39:1--21, 2012. [ .pdf \| Abstract ]
[6]	Paul R. Willems and Bruno Lang. Twisted factorizations and qd-type transformations for the MR³ algorithm---new representations and analysis. SIAM J. Matrix Anal. Appl., 33(2):523--553, 2012. [ DOI \| Abstract ]
[7]	T. Auckenthaler, V. Blum, H.-J. Bungartz, T. Huckle, R. Johanni, L. Krämer, B. Lang, H. Lederer, and P. R. Willems. Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations. Parallel Comput., 37(12):783--794, December 2011. [ DOI \| Abstract ]
[8]	Martin Galgon, Lukas Krämer, and Bruno Lang. The FEAST algorithm for large sparse eigenvalue problems. Proc. Appl. Math. Mech., 11(1):747--748, December 2011. [ DOI \| Abstract ]
[9]	T. Auckenthaler, H.-J. Bungartz, T. Huckle, L. Krämer, B. Lang, and P. Willems. Developing algorithms and software for the parallel solution of the symmetric eigenvalue problem. J. Comput. Sci., 2(3):272--278, August 2011. [ DOI \| Abstract ]
[10]	Paul R. Willems and Bruno Lang. Block factorizations and qd-type transformations for the MR³ algorithm. Electron. Trans. Numer. Anal., 38:363--400, 2011. [ .pdf \| Abstract ]

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