DFT-FE – A massively parallel adaptive finite-element code for large-scale density functional theory calculations

Abstract

We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for largescale ab-initio calculations (reaching ∼ 100, 000 electrons) using Kohn-Sham density functional theory (DFT). DFT-FE is based on a local real-space variational formulation of the Kohn-Sham DFT energy functional that is discretized using a higher-order adaptive spectral finite-element (FE) basis, and treats pseudopotential and all-electron calculations in the same framework, while accommodating non-periodic, semi-periodic and periodic boundary conditions. We discuss the main aspects of the code, which include, the various strategies of adaptive FE basis generation, and the different approaches employed in the numerical implementation of the solution of the discrete Kohn-Sham problem that are focused on significantly reducing the floating point operations, communication costs and latency. We demonstrate the accuracy of DFT-FE by comparing the energies, ionic forces and periodic cell stresses on a wide range of problems with popularly used DFT codes. Further, we demonstrate that DFT-FE significantly outperforms widely used planewave codes-both in CPU-times and wall-times, and on both non-periodic and periodic systems-at systems sizes beyond a few thousand electrons, with over 5 − 10 fold speedups in systems with more than 10,000 electrons. The benchmark studies also highlight the excellent parallel scalability of DFT-FE, with strong scaling demonstrated on up to 192,000 MPI tasks.

PRISMS-Fatigue computational framework for fatigue analysis in polycrystalline metals and alloys

“…Five applications demonstrated the performance and flexibility of PRISMS-Fatigue in capturing the fatigue crack formation driving force: different crystallographic textures, grain morphologies, multiaxial strain states and magnitudes using a computational multiaxial Gamma (Γ) Plane, boundary conditions, and sample sizes. Maximizing the downstream value of PRISMS-Fatigue depends on contributions from the research community analogous to other material science and mechanics platforms (e.g., PRISMS-PF 32 , DFT-FE 28 , CASM 29 , and LAMMPS 30 ). Thus, the link between PRISMS-Fatigue and Materials Commons will focus on facilitating continuous improvement in the framework as an efficient, flexible, scalable, and modular tool.…”

“…An alternative paradigm more commonly pursued in modern digital materials science is based on developing an open-source framework, which can be used and/or modified by the fatigue community. In this regard examples in related materials research communities include Density-functional theory (DFT) calculations (DFT-FE 28 ), first-principles statistical mechanics (CASM 29 ), atomistic simulation (LAMMPS 30 ), crystal plasticity finite element method (CPFEM) codes (PRISMS-Plasticity 31 ), and phase-field codes (PRISMS-PF 32 ). Developing an open-source fatigue framework for microstructurescale comparisons broadens the community of research to investigate complex fatigue-related problems, with a focus on developing other features rather than reimplementing basic elements of the framework in limited-use, homegrown codes and subroutines.…”

On preconditioning the self-consistent field iteration in real-space Density Functional Theory

“…6 and 7 recovers the real-space Kerker preconditoner-implementation within existing real-space codes is straightforward. Also, though the focus here is on the finite-difference discretization, the proposed approach is expected to be applicable to other real-space techniques such as the finite-element method [34,35,36].…”

Proxima

“…These applications are often dominated by the repetitive execution of a few high-cost functions [6,22]. In the past, speedups in these domains have relied on advances in hardware architecture and numerical-algorithm development [18,21,35]. However, recent advances in machine learning have enabled another promising acceleration technique: replacing expensive functions with machine-learned surrogates [4,15].…”