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Title: SQDFT: Spectral Quadrature method for large-scale parallel O ( N ) Kohn–Sham calculations at high temperature

Abstract

We present SQDFT: a large-scale 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 finite-difference implementation of the infinite-cell 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 self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.

Authors:
 [1];  [1];  [1];  [2]
  1. Georgia Inst. of Technology, Atlanta, GA (United States). College of Engineering
  2. 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):
LLNL-JRNL-738006
Journal ID: ISSN 0010-4655; TRN: US1900520
Grant/Contract Number:  
AC52-07NA27344; 1333500
Resource Type:
Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 224; Journal Issue: C; Journal ID: ISSN 0010-4655
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 large-scale 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 large-scale 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 large-scale 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 large-scale 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 large-scale 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 finite-difference implementation of the infinite-cell 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 self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale 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}
}

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Figure-1 Figure-1: Outline of quantum molecular dynamics (QMD) simulation.

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