ELPA: A parallel solver for the generalized eigenvalue problem

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; Christoph Scheurer

doi:10.3233/APC200095

ELPA: A parallel solver for the generalized eigenvalue problem

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, Christoph Scheurer

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

For symmetric (hermitian) (dense or banded) matrices the computation of eigenvalues and eigenvectors Ax = λBx is an important task, e.g. in electronic structure calculations. If a larger number of eigenvectors are needed, often direct solvers are applied. On parallel architectures the ELPA implementation has proven to be very efficient, also compared to other parallel solvers like EigenExa or MAGMA. The main improvement that allows better parallel efficiency in ELPA is the two-step transformation of dense to band to tridiagonal form. This was the achievement of the ELPA project. The continuation of this project has been targeting at additional improvements like allowing monitoring and autotuning of the ELPA code, optimizing the code for different architectures, developing curtailed algorithms for banded A and B, and applying the improved code to solve typical examples in electronic structure calculations. In this paper we will present the outcome of this project.

Original language	English
Title of host publication	Parallel Computing
Subtitle of host publication	Technology Trends
Editors	Ian Foster, Gerhard R. Joubert, Ludek Kucera, Wolfgang E. Nagel, Frans Peters
Publisher	IOS Press BV
Pages	647-668
Number of pages	22
ISBN (Electronic)	9781643680705
DOIs	https://doi.org/10.3233/APC200095
State	Published - 2020

Publication series

Name	Advances in Parallel Computing
Volume	36
ISSN (Print)	0927-5452
ISSN (Electronic)	1879-808X

Keywords

ELPA-AEO
Eigensolver
Electronic structure calculations
Parallel

Access to Document

10.3233/APC200095

Cite this

Bungartz, H. J., Carbogno, C., Galgon, M., Huckle, T., Köcher, S., Kowalski, H. H., Kus, P., Lang, B., Lederer, H., Manin, V., Marek, A., Reuter, K., Rippl, M., Scheffler, M., & Scheurer, C. (2020). ELPA: A parallel solver for the generalized eigenvalue problem. In I. Foster, G. R. Joubert, L. Kucera, W. E. Nagel, & F. Peters (Eds.), Parallel Computing: Technology Trends (pp. 647-668). (Advances in Parallel Computing; Vol. 36). IOS Press BV. https://doi.org/10.3233/APC200095

@inproceedings{a4129d066dda448d9ef4d4a8bc243d01,

title = "ELPA: A parallel solver for the generalized eigenvalue problem",

abstract = "For symmetric (hermitian) (dense or banded) matrices the computation of eigenvalues and eigenvectors Ax = λBx is an important task, e.g. in electronic structure calculations. If a larger number of eigenvectors are needed, often direct solvers are applied. On parallel architectures the ELPA implementation has proven to be very efficient, also compared to other parallel solvers like EigenExa or MAGMA. The main improvement that allows better parallel efficiency in ELPA is the two-step transformation of dense to band to tridiagonal form. This was the achievement of the ELPA project. The continuation of this project has been targeting at additional improvements like allowing monitoring and autotuning of the ELPA code, optimizing the code for different architectures, developing curtailed algorithms for banded A and B, and applying the improved code to solve typical examples in electronic structure calculations. In this paper we will present the outcome of this project.",

keywords = "ELPA-AEO, Eigensolver, Electronic structure calculations, Parallel",

author = "Bungartz, {Hans Joachim} and Christian Carbogno and Martin Galgon and Thomas Huckle and Simone K{\"o}cher and Kowalski, {Hagen Henrik} and Pavel Kus and Bruno Lang and Hermann Lederer and Valeriy Manin and Andreas Marek and Karsten Reuter and Michael Rippl and Matthias Scheffler and Christoph Scheurer",

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year = "2020",

doi = "10.3233/APC200095",

language = "English",

series = "Advances in Parallel Computing",

publisher = "IOS Press BV",

pages = "647--668",

editor = "Ian Foster and Joubert, {Gerhard R.} and Ludek Kucera and Nagel, {Wolfgang E.} and Frans Peters",

booktitle = "Parallel Computing",

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Bungartz, HJ, Carbogno, C, Galgon, M, Huckle, T, Köcher, S, Kowalski, HH, Kus, P, Lang, B, Lederer, H, Manin, V, Marek, A, Reuter, K, Rippl, M, Scheffler, M & Scheurer, C 2020, ELPA: A parallel solver for the generalized eigenvalue problem. in I Foster, GR Joubert, L Kucera, WE Nagel & F Peters (eds), Parallel Computing: Technology Trends. Advances in Parallel Computing, vol. 36, IOS Press BV, pp. 647-668. https://doi.org/10.3233/APC200095

ELPA: A parallel solver for the generalized eigenvalue problem. / Bungartz, Hans Joachim; Carbogno, Christian; Galgon, Martin et al.
Parallel Computing: Technology Trends. ed. / Ian Foster; Gerhard R. Joubert; Ludek Kucera; Wolfgang E. Nagel; Frans Peters. IOS Press BV, 2020. p. 647-668 (Advances in Parallel Computing; Vol. 36).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T2 - A parallel solver for the generalized eigenvalue problem

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AU - Carbogno, Christian

AU - Galgon, Martin

AU - Huckle, Thomas

AU - Köcher, Simone

AU - Kowalski, Hagen Henrik

AU - Kus, Pavel

AU - Lang, Bruno

AU - Lederer, Hermann

AU - Manin, Valeriy

AU - Marek, Andreas

AU - Reuter, Karsten

AU - Rippl, Michael

AU - Scheffler, Matthias

AU - Scheurer, Christoph

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AB - For symmetric (hermitian) (dense or banded) matrices the computation of eigenvalues and eigenvectors Ax = λBx is an important task, e.g. in electronic structure calculations. If a larger number of eigenvectors are needed, often direct solvers are applied. On parallel architectures the ELPA implementation has proven to be very efficient, also compared to other parallel solvers like EigenExa or MAGMA. The main improvement that allows better parallel efficiency in ELPA is the two-step transformation of dense to band to tridiagonal form. This was the achievement of the ELPA project. The continuation of this project has been targeting at additional improvements like allowing monitoring and autotuning of the ELPA code, optimizing the code for different architectures, developing curtailed algorithms for banded A and B, and applying the improved code to solve typical examples in electronic structure calculations. In this paper we will present the outcome of this project.

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A2 - Nagel, Wolfgang E.

A2 - Peters, Frans

PB - IOS Press BV

ER -

ELPA: A parallel solver for the generalized eigenvalue problem

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