State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems

Christof Vömel; Stanimire Z. Tomov; Osni A. Marques; A. Canning; Lin Wang Wang; Jack J. Dongarra

doi:10.1016/j.jcp.2008.01.018

State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems

Christof Vömel
, Stanimire Z. Tomov
, Osni A. Marques
, A. Canning
, Lin Wang Wang
, Jack J. Dongarra

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

The band edge states determine optical and electronic properties of semiconductor nano-structures which can be computed from an interior eigenproblem. We study the reliability and performance of state-of-the-art iterative eigensolvers on large quantum dots and wires, focusing on variants of preconditioned CG, Lanczos, and Davidson methods. One Davidson variant, the GD + k (Olsen) method, is identified to be as reliable as the commonly used preconditioned CG while consistently being between two and three times faster.

Original language	English
Pages (from-to)	7113-7124
Number of pages	12
Journal	Journal of Computational Physics
Volume	227
Issue number	15
DOIs	https://doi.org/10.1016/j.jcp.2008.01.018
State	Published - Jul 20 2008
Externally published	Yes

Funding

This work was supported by the US Department of Energy under LAB03-17 initiative, Contract Nos. DE-FG02-03ER25584 and DE-AC03-76SF00098.

Keywords

Computational nano-technology
Davidson's method
Electronic structure
Implicitly restarted Arnoldi
Preconditioned conjugate gradients

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10.1016/j.jcp.2008.01.018

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title = "State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems",

abstract = "The band edge states determine optical and electronic properties of semiconductor nano-structures which can be computed from an interior eigenproblem. We study the reliability and performance of state-of-the-art iterative eigensolvers on large quantum dots and wires, focusing on variants of preconditioned CG, Lanczos, and Davidson methods. One Davidson variant, the GD + k (Olsen) method, is identified to be as reliable as the commonly used preconditioned CG while consistently being between two and three times faster.",

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AU - Vömel, Christof

AU - Tomov, Stanimire Z.

AU - Marques, Osni A.

AU - Canning, A.

AU - Wang, Lin Wang

AU - Dongarra, Jack J.

PY - 2008/7/20

Y1 - 2008/7/20

N2 - The band edge states determine optical and electronic properties of semiconductor nano-structures which can be computed from an interior eigenproblem. We study the reliability and performance of state-of-the-art iterative eigensolvers on large quantum dots and wires, focusing on variants of preconditioned CG, Lanczos, and Davidson methods. One Davidson variant, the GD + k (Olsen) method, is identified to be as reliable as the commonly used preconditioned CG while consistently being between two and three times faster.

AB - The band edge states determine optical and electronic properties of semiconductor nano-structures which can be computed from an interior eigenproblem. We study the reliability and performance of state-of-the-art iterative eigensolvers on large quantum dots and wires, focusing on variants of preconditioned CG, Lanczos, and Davidson methods. One Davidson variant, the GD + k (Olsen) method, is identified to be as reliable as the commonly used preconditioned CG while consistently being between two and three times faster.

KW - Computational nano-technology

KW - Davidson's method

KW - Electronic structure

KW - Implicitly restarted Arnoldi

KW - Preconditioned conjugate gradients

UR - https://www.scopus.com/pages/publications/45449103623

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M3 - Article

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SP - 7113

EP - 7124

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 15

ER -

State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems

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Keywords

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