Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for largescale electronic structure calculations
The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the KohnSham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated onthefly 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 largescale 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 largescale 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 twodimensional parallelization scheme, thanks to the orthogonality of the DG basis set and blocksparse structure of the DG Hamiltonian matrix. The onthefly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DGCheFSI approach in calculations of largescale twodimensional graphene sheets and bulk threedimensional lithiumion electrolyte systems. In conclusion, employing 55 296more »
 Authors:

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 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Divisio; Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Divisio
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physics Division
 Publication Date:
 Report Number(s):
 LLNLJRNL735618
Journal ID: ISSN 00219606
 Grant/Contract Number:
 AC5207NA27344; AC52 07NA27344; AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 145; Journal Issue: 15; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
 OSTI Identifier:
 1438776
 Alternate Identifier(s):
 OSTI ID: 1420728; OSTI ID: 1456961
Banerjee, Amartya S., Lin, Lin, Hu, Wei, Yang, Chao, and Pask, John E.. Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for largescale electronic structure calculations. United States: N. p.,
Web. doi:10.1063/1.4964861.
Banerjee, Amartya S., Lin, Lin, Hu, Wei, Yang, Chao, & Pask, John E.. Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for largescale electronic structure calculations. United States. doi:10.1063/1.4964861.
Banerjee, Amartya S., Lin, Lin, Hu, Wei, Yang, Chao, and Pask, John E.. 2016.
"Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for largescale electronic structure calculations". United States.
doi:10.1063/1.4964861. https://www.osti.gov/servlets/purl/1438776.
@article{osti_1438776,
title = {Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for largescale electronic structure calculations},
author = {Banerjee, Amartya S. and Lin, Lin and Hu, Wei and Yang, Chao and Pask, John E.},
abstractNote = {The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the KohnSham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated onthefly 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 largescale 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 largescale 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 twodimensional parallelization scheme, thanks to the orthogonality of the DG basis set and blocksparse structure of the DG Hamiltonian matrix. The onthefly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DGCheFSI approach in calculations of largescale twodimensional graphene sheets and bulk threedimensional lithiumion electrolyte systems. In conclusion, employing 55 296 computational cores, the time per selfconsistent 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.},
doi = {10.1063/1.4964861},
journal = {Journal of Chemical Physics},
number = 15,
volume = 145,
place = {United States},
year = {2016},
month = {10}
}
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