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

## TL;DR

DFT-FE is a highly scalable, accurate finite-element code for large-scale density functional theory calculations, outperforming traditional plane-wave methods in speed and efficiency for systems with thousands of electrons.

## Contribution

This work introduces DFT-FE, a massively parallel finite-element DFT code that handles large systems efficiently with adaptive basis and reduced computational costs.

## Key findings

- Achieves over 5-10x speedup compared to plane-wave codes for systems with >10,000 electrons.
- Demonstrates strong parallel scalability up to 192,000 MPI tasks.
- Maintains high accuracy in energies, forces, and stresses across diverse systems.

## Abstract

We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching $\sim 100,000$ 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 plane-wave 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.