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

We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching similar to 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 up to 192,000 MPI tasks. Program summary Program Title: DFT-FE Program Files doi : http://dx.doi.org/10.17632/tgdmgvmfft.1 Licensing provisions: LGPL v3 Programming language: C/C++ External routines/libraries: p4est (http://www.p4est.org/), deal.II (https://www.dealii.org/), BLAS (http://www.netlib.org/blas/), LAPACK (http://www.netlib.orgflapack/), ELPA (https://elpa.mpcdf.mpg.de/), ScaLAPACK (http://www.netlib.org/scalapack/), Spglib (https://atztogo.github.io/spglib/), ALGLIB (http://www.alglib.net/), LIBXC (http://www.tddft.orgiprograms/libxc/). PETSc (https://www.mcs.anl.gov/petsc), SLEPc (http://slepc.upv.es). Nature of problem: Density functional theory calculations. Solution method: We employ a local real-space variational formulation of Kohn-Sham density functional theory that is applicable for both pseudopotential and all-electron calculations with arbitrary boundary conditions. Higher-order adaptive spectral finite-element basis is used to discretize the Kohn-Sham equations. Chebyshev polynomial filtered subspace iteration procedure (ChFSI) is employed to solve the nonlinear Kohn-Sham eigenvalue problem self-consistently. ChFSI in DFT-FE employs Cholesky factorization based orthonormalization, and spectrum splitting based Rayleigh-Ritz procedure in conjunction with mixed precision arithmetic. Configurational force approach is used to compute ionic forces and periodic cell stresses for geometry optimization. Restrictions: Exchange-correlation functionals are restricted to Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA), with and without spin. The pseudopotentials available are optimized norm conserving Vanderbilt (ONCV) pseudopotentials and Troullier-Martins (TM) pseudopotentials. Calculations are non-relativistic. Unusual features: DFT-FE handles all-electron and pseudopotential calculations in the same framework, while accommodating periodic, non-periodic and semi-periodic boundary conditions. Additional comments: DFT-FE github https://github.com/dftfeDevelopers/dftfe (C) 2019 Elsevier B.V. All rights reserved.