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Title: Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

Journal Article · · Journal of Computational Chemistry
DOI:https://doi.org/10.1002/jcc.24254· OSTI ID:1248169
 [1];  [1];  [2];  [1];  [1]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Univ. of Alabama, Tuscaloosa, AL (United States)

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ~330,000 (~5600) eigenvalues and eigenfunctions are obtained in ~190 (~5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPs is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. As a result, a parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
1248169
Journal Information:
Journal of Computational Chemistry, Vol. 37, Issue 4; ISSN 0192-8651
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 13 works
Citation information provided by
Web of Science

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Cited By (5)

Three pillars for achieving quantum mechanical molecular dynamics simulations of huge systems: Divide-and-conquer, density-functional tight-binding, and massively parallel computation journal June 2016
Three-body expansion of the fragment molecular orbital method combined with density-functional tight-binding journal January 2017
SIESTA-SIPs: Massively parallel spectrum-slicing eigensolver for an ab initio molecular dynamics package journal August 2018
On the achievement of high fidelity and scalability for large-scale diagonalizations in grid-based DFT simulations journal March 2018
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