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Shift‐and‐invert parallel spectral transformation eigensolver: Massively parallel performance for density‐functional based tight‐binding
Author(s) -
Keçeli Murat,
Zhang Hong,
Zapol Peter,
Dixon David A.,
Wagner Albert F.
Publication year - 2016
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.24254
Subject(s) - massively parallel , eigenvalues and eigenvectors , scaling , eigenfunction , density functional theory , scalability , tight binding , hamiltonian (control theory) , eigendecomposition of a matrix , diamond , parallel computing , computational science , computer science , physics , materials science , mathematics , quantum mechanics , mathematical optimization , electronic structure , geometry , database , composite material
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. A parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated. © 2015 Wiley Periodicals, Inc.