Two-level Chebyshev filter based complementary subspace method: pushing
the envelope of large-scale electronic structure calculations

Amartya S. Banerjee, Lin Lin, Phanish Suryanarayana, Chao Yang, John E. Pask

Published:

We describe a novel iterative strategy for Kohn-Sham density functional
theory calculations aimed at large systems (> 1000 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 seconds on 34,560 processors; thus allowing us to carry out 1.0
ps of ab initio molecular dynamics in approximately 28 hours (of wall time).