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Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations

Journal Article · · Journal of Chemical Theory and Computation
 [1];  [2];  [3];  [1];  [4]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
  2. Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
  3. Georgia Inst. of Technology, Atlanta, GA (United States). College of Engineering
  4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physics Division
+ Show Author Affiliations
We describe here a novel iterative strategy for Kohn–Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn–Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).
Research Organization:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States)
Sponsoring Organization:
National Science Foundation (NSF) (United States); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
AC02-05CH11231; AC52-07NA27344; SC0017867
OSTI ID:
1512626
Alternate ID(s):
OSTI ID: 1526530
Report Number(s):
LLNL-JRNL--757223; 943724
Journal Information:
Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 6 Vol. 14; ISSN 1549-9618
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (3)

A Shift Selection Strategy for Parallel Shift-invert Spectrum Slicing in Symmetric Self-consistent Eigenvalue Computation journal November 2020
Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-IV nanotubes journal September 2019
Quantum Dynamics at Scale: Ultrafast Control of Emergent Functional Materials
  • Tiwari, Subodh C.; Krishnamoorthy, Aravind; Rajak, Pankaj
  • HPCAsia2020: International Conference on High Performance Computing in Asia-Pacific Region, Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region https://doi.org/10.1145/3368474.3368489
conference January 2020

Figures / Tables (10)

Table 1(p. 26)table Table 1
Figure 1(p. 27)figure Figure 1
Table 2(p. 29)table Table 2
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Figure 3(p. 35)figure Figure 3
Figure 4(p. 36)figure Figure 4
Figure 5(p. 38)figure Figure 5
Table 4(p. 40)table Table 4
Figure 6(p. 42)figure Figure 6

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