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

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.
 [1] ;  [1] ;  [2] ;  [1] ;  [1]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Univ. of Alabama, Tuscaloosa, AL (United States)
Publication Date:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of Computational Chemistry
Additional Journal Information:
Journal Volume: 37; Journal Issue: 4; Journal ID: ISSN 0192-8651
Research Org:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences, and Biosciences Division
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; sparse matrices; spectrum slicing; generalized eigenvalue problem; semi-empirical methods; tight-binding DFT
OSTI Identifier: