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Title: Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4964861· OSTI ID:1438776
 [1];  [2]; ORCiD logo [3];  [3];  [4]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Divisio; Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Divisio
  4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physics Division
+ Show Author Affiliations

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials' simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC52-07NA27344; AC52- 07NA27344; AC02-05CH11231
OSTI ID:
1438776
Alternate ID(s):
OSTI ID: 1420728; OSTI ID: 1456961
Report Number(s):
LLNL-JRNL-735618; TRN: US1900523
Journal Information:
Journal of Chemical Physics, Vol. 145, Issue 15; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 26 works
Citation information provided by
Web of Science

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Cited By (8)

Ab initio simulations of liquid electrolytes for energy conversion and storage journal October 2018
Orbital-enriched flat-top partition of unity method for the Schrödinger eigenproblem journal December 2018
ELSI — An open infrastructure for electronic structure solvers journal November 2020
Task-based Parallel Computation of the Density Matrix in Quantum-based Molecular Dynamics using Graph Partitioning journal January 2017
Interpolative Separable Density Fitting through Centroidal Voronoi Tessellation With Applications to Hybrid Functional Electronic Structure Calculations preprint January 2017
ChASE: Chebyshev Accelerated Subspace iteration Eigensolver for sequences of Hermitian eigenvalue problems preprint January 2018
Discontinuous Galerkin discretization for quantum simulation of chemistry preprint January 2019
A Parallel Direct Eigensolver for Sequences of Hermitian Eigenvalue Problems with No Tridiagonalization preprint January 2020

Figures / Tables (11)

FIG. 1(p. 12)figure FIG. 1
Algorithm 1(p. 15)figure Algorithm 1
FIG. 2(p. 16)figure FIG. 2
FIG. 3(p. 21)figure FIG. 3
FIG. 4(p. 22)figure FIG. 4
FIG. 5(p. 25)figure FIG. 5
FIG. 6(p. 26)figure FIG. 6
FIG. 7(p. 28)figure FIG. 7
FIG. 8(p. 29)figure FIG. 8
TABLE I(p. 30)table TABLE I
TABLE II(p. 31)table TABLE II

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