DGDFT: A Massively Parallel Method for Large Scale Density Functional Theory Calculations

TL;DR

DGDFT is a highly parallelized, efficient large-scale DFT method using adaptive local basis functions, achieving near-planewave accuracy with fewer degrees of freedom and excellent scalability on supercomputers.

Contribution

The paper introduces a massively parallel implementation of DGDFT with adaptive basis functions, enabling scalable large-scale electronic structure calculations with reduced computational cost.

Findings

Achieves 80% parallel efficiency on 128,000 cores

Handles systems with 3,500-14,000 atoms effectively

Scales at most quadratically with the number of electrons

Abstract

We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) [J. Comput. Phys. 2012, 231, 2140] 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.