DGDFT: A massively parallel method for large scale density functional theory calculations

Abstract

We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) method, for efficient large-scale Kohn-Sham DFT based electronic structure calculations. The DGDFT method uses adaptive local basis (ALB) functions generated on-the-fly during the self-consistent field (SCF) iteration to represent the solution to the Kohn-Sham equations. The use of the ALB set provides a systematic way to improve the accuracy of the approximation. It minimizes the number of degrees of freedom required to represent the solution to the Kohn-Sham problem for a desired level of accuracy. In particular, DGDFT can reach the planewave accuracy with far fewer numbers of degrees of freedom. By using the pole expansion and selected inversion (PEXSI) technique to compute electron density, energy and atomic forces, we can make the computational complexity of DGDFT scale at most quadratically with respect to the number of electrons for both insulating and metallic systems. We show that DGDFT can achieve 80% parallel efficiency on 128,000 high performance computing cores when it is used to study the electronic structure of two-dimensional (2D) phosphorene systems with 3,500-14,000 atoms. This high parallel efficiency results from a two-level parallelization scheme that we will describe in detail.

Fast Real-Time Time-Dependent Density Functional Theory Calculations with the Parallel Transport Gauge

“…Our method is implemented in PWDFT code, which uses the planewave basis set and is a self-contained module in the massively parallel DGDFT (Discontinuous Galerkin Density Functional Theory) software package. 12,13 We use the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional, 14 and the Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials. 15,16 The first example is the computation of the absorption spectrum of an anthracene molecule.…”

Applications of large-scale density functional theory in biology

“…Similar topics have been investigated by VandeVondele et al in the context of the CP2K code [76]. There have been recent proposals for DFT methodologies and basis sets whose main virtues are that they can be efficiently parallelised to very large numbers of cores [77].…”

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

“…For electronic structure calculations, the PEXSI package is also integrated into the recently developed "Electronic Structure Infrastructure" (ELSI) software package 1 . In order to demonstrate that the performance of the new method in the context of SCF iterations for real materials, we test its performance in the DGDFT (Discontinuous Galerkin Density Functional Theory) software package 12,23 , which is a massively parallel electronic structure software package for large scale DFT calculations using adaptive local basis functions (ALB).…”