SQDFT: Spectral Quadrature method for largescale parallel $\mathcal{O}\left(N\right)$ Kohn–Sham calculations at high temperature
Abstract
We present SQDFT: a largescale parallel implementation of the Spectral Quadrature (SQ) method for $$\mathscr{O}(N)$$ Kohn–Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finitedifference implementation of the infinitecell Clenshaw–Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. Here, we further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect $$\mathscr{O}(N)$$ scaling with system size and wall times as low as a few seconds per selfconsistent field iteration. Finally, we verify the accuracy of SQDFT in largescale quantum molecular dynamics simulations of aluminum at high temperature.
 Authors:

 Georgia Inst. of Technology, Atlanta, GA (United States). College of Engineering
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physics Division
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE; National Science Foundation (NSF)
 OSTI Identifier:
 1438771
 Report Number(s):
 LLNLJRNL738006
Journal ID: ISSN 00104655; TRN: US1900520
 Grant/Contract Number:
 AC5207NA27344; 1333500
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 224; Journal Issue: C; Journal ID: ISSN 00104655
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICS AND COMPUTING
Citation Formats
Suryanarayana, Phanish, Pratapa, Phanisri P., Sharma, Abhiraj, and Pask, John E. SQDFT: Spectral Quadrature method for largescale parallel O(N) Kohn–Sham calculations at high temperature. United States: N. p., 2017.
Web. doi:10.1016/j.cpc.2017.12.003.
Suryanarayana, Phanish, Pratapa, Phanisri P., Sharma, Abhiraj, & Pask, John E. SQDFT: Spectral Quadrature method for largescale parallel O(N) Kohn–Sham calculations at high temperature. United States. doi:10.1016/j.cpc.2017.12.003.
Suryanarayana, Phanish, Pratapa, Phanisri P., Sharma, Abhiraj, and Pask, John E. Thu .
"SQDFT: Spectral Quadrature method for largescale parallel O(N) Kohn–Sham calculations at high temperature". United States. doi:10.1016/j.cpc.2017.12.003. https://www.osti.gov/servlets/purl/1438771.
@article{osti_1438771,
title = {SQDFT: Spectral Quadrature method for largescale parallel O(N) Kohn–Sham calculations at high temperature},
author = {Suryanarayana, Phanish and Pratapa, Phanisri P. and Sharma, Abhiraj and Pask, John E.},
abstractNote = {We present SQDFT: a largescale parallel implementation of the Spectral Quadrature (SQ) method for $\mathscr{O}(N)$ Kohn–Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finitedifference implementation of the infinitecell Clenshaw–Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. Here, we further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect $\mathscr{O}(N)$ scaling with system size and wall times as low as a few seconds per selfconsistent field iteration. Finally, we verify the accuracy of SQDFT in largescale quantum molecular dynamics simulations of aluminum at high temperature.},
doi = {10.1016/j.cpc.2017.12.003},
journal = {Computer Physics Communications},
number = C,
volume = 224,
place = {United States},
year = {2017},
month = {12}
}
Web of Science
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