research-article

ChASE: Chebyshev Accelerated Subspace Iteration Eigensolver for Sequences of Hermitian Eigenvalue Problems

Authors:

Jan Winkelmann,

Edoardo Di NapoliAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 45, Issue 2

Article No.: 21, Pages 1 - 34

https://doi.org/10.1145/3313828

Published: 26 April 2019 Publication History

Abstract

Solving dense Hermitian eigenproblems arranged in a sequence with direct solvers fails to take advantage of those spectral properties that are pertinent to the entire sequence and not just to the single problem. When such features take the form of correlations between the eigenvectors of consecutive problems, as is the case in many real-world applications, the potential benefit of exploiting them can be substantial. We present the Chebyshev Accelerated Subspace iteration Eigensolver (ChASE), a modern algorithm and library based on subspace iteration with polynomial acceleration. Novel to ChASE is the computation of the spectral estimates that enter in the filter and an optimization of the polynomial degree that further reduces the necessary floating-point operations. ChASE is written in C++ using the modern software engineering concepts that favor a simple integration in application codes and a straightforward portability over heterogeneous platforms. When solving sequences of Hermitian eigenproblems for a portion of their extremal spectrum, ChASE greatly benefits from the sequence’s spectral properties and outperforms direct solvers in many scenarios. The library ships with two distinct parallelization schemes, supports execution over distributed GPUs, and is easily extensible to other parallel computing architectures.

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Cited By

Wu XDi Napoli E(2023)Advancing the distributed Multi-GPU ChASE library through algorithm optimization and NCCL libraryProceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis10.1145/3624062.3624249(1688-1696)Online publication date: 12-Nov-2023
https://dl.acm.org/doi/10.1145/3624062.3624249
Alvermann AHager GFehske H(2023)Orthogonal Layers of Parallelism in Large-Scale Eigenvalue ComputationsACM Transactions on Parallel Computing10.1145/361444410:3(1-31)Online publication date: 22-Sep-2023
https://dl.acm.org/doi/10.1145/3614444
Zhang YLi SYuan FDong DYang XLi TWang Z(2023)Memory-aware Optimization for Sequences of Sparse Matrix-Vector Multiplications2023 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS54959.2023.00046(379-389)Online publication date: May-2023
https://doi.org/10.1109/IPDPS54959.2023.00046
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Index Terms

ChASE: Chebyshev Accelerated Subspace Iteration Eigensolver for Sequences of Hermitian Eigenvalue Problems

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 45, Issue 2

June 2019

255 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3326465

Editors:
Zhaojun Bai
University of California at Davis, USA
,
Wolfgang Bangerth
Colorado State University, USA

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Copyright © 2019 ACM.

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Publication History

Published: 26 April 2019

Accepted: 01 February 2019

Revised: 01 November 2018

Received: 01 May 2018

Published in TOMS Volume 45, Issue 2

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Cited By

Wu XDi Napoli E(2023)Advancing the distributed Multi-GPU ChASE library through algorithm optimization and NCCL libraryProceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis10.1145/3624062.3624249(1688-1696)Online publication date: 12-Nov-2023
https://dl.acm.org/doi/10.1145/3624062.3624249
Alvermann AHager GFehske H(2023)Orthogonal Layers of Parallelism in Large-Scale Eigenvalue ComputationsACM Transactions on Parallel Computing10.1145/361444410:3(1-31)Online publication date: 22-Sep-2023
https://dl.acm.org/doi/10.1145/3614444
Zhang YLi SYuan FDong DYang XLi TWang Z(2023)Memory-aware Optimization for Sequences of Sparse Matrix-Vector Multiplications2023 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS54959.2023.00046(379-389)Online publication date: May-2023
https://doi.org/10.1109/IPDPS54959.2023.00046
Dawson WKawashima ERatcliff LKamiya MGenovese LNakajima T(2023)Complexity reduction in density functional theory: Locality in space and energyThe Journal of Chemical Physics10.1063/5.0142652158:16Online publication date: 27-Apr-2023
https://doi.org/10.1063/5.0142652
Wu XDavidović DAchilles SDi Napoli ERobinson T(2022)ChASEProceedings of the Platform for Advanced Scientific Computing Conference10.1145/3539781.3539792(1-12)Online publication date: 27-Jun-2022
https://dl.acm.org/doi/10.1145/3539781.3539792
Liou KBiller AKronik LChelikowsky J(2021)Space-Filling Curves for Real-Space Electronic Structure CalculationsJournal of Chemical Theory and Computation10.1021/acs.jctc.1c0023717:7(4039-4048)Online publication date: 3-Jun-2021
https://doi.org/10.1021/acs.jctc.1c00237
Zhang XAchilles SWinkelmann JHaas RSchleife ADi Napoli E(2021)Solving the Bethe-Salpeter equation on massively parallel architecturesComputer Physics Communications10.1016/j.cpc.2021.108081267(108081)Online publication date: Oct-2021
https://doi.org/10.1016/j.cpc.2021.108081
Singer SNapoli ENovaković VČaklović G(2020)The LAPW Method with Eigendecomposition Based on the Hari--Zimmermann Generalized Hyperbolic SVDSIAM Journal on Scientific Computing10.1137/19M127781342:5(C265-C293)Online publication date: 21-Sep-2020
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Yu VCampos CDawson WGarcía AHavu VHourahine BHuhn WJacquelin MJia WKeçeli MLaasner RLi YLin LLu JMoussa JRoman JVázquez-Mayagoitia ÁYang CBlum V(2020)ELSI — An open infrastructure for electronic structure solversComputer Physics Communications10.1016/j.cpc.2020.107459256(107459)Online publication date: Nov-2020
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Liou KYang CChelikowsky J(2020)Scalable implementation of polynomial filtering for density functional theory calculation in PARSECComputer Physics Communications10.1016/j.cpc.2020.107330(107330)Online publication date: Apr-2020
https://doi.org/10.1016/j.cpc.2020.107330
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