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

摘要

We describe a novel iterative strategy for Kohn-Sham density functionaltheory calculations aimed at large systems (> 1000 electrons), applicable tometals and insulators alike. In lieu of explicit diagonalization of theKohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employa two-level Chebyshev polynomial filter based complementary subspace strategyto: 1) compute a set of vectors that span the occupied subspace of theHamiltonian; 2) reduce subspace diagonalization to just partially occupiedstates; and 3) obtain those states in an efficient, scalable manner via aninner Chebyshev-filter iteration. By reducing the necessary computation to justpartially occupied states, and obtaining these through an inner Chebysheviteration, our approach reduces the cost of large metallic calculationssignificantly, while eliminating subspace diagonalization for insulatingsystems altogether. We describe the implementation of the method within theframework of the Discontinuous Galerkin (DG) electronic structure method andshow that this results in a computational scheme that can effectively tacklebulk and nano systems containing tens of thousands of electrons, with chemicalaccuracy, within a few minutes or less of wall clock time per SCF iteration onlarge-scale computing platforms. We anticipate that our method will beinstrumental in pushing the envelope of large-scale ab initio moleculardynamics. As a demonstration of this, we simulate a bulk silicon systemcontaining 8,000 atoms at finite temperature, and obtain an average SCF stepwall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0ps of ab initio molecular dynamics in approximately 28 hours (of wall time).