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

Abstract

We present a real-space formulation for isotropic Fourier-space preconditioners used to accelerate the self-consistent field iteration in Density Functional Theory calculations. Specifically, after approximating the preconditioner in Fourier space using a rational function, we express its realspace application in terms of the solution of sparse Helmholtz-type systems. Using the truncated-Kerker and Resta preconditioners as representative examples, we show that the proposed realspace method is both accurate and efficient, requiring the solution of a single linear system, while accelerating self-consistency to the same extent as its exact Fourier-space counterpart.

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

“…This is motivated from the observation that the calculation of spectral quadrature weights and nodes -the computationally dominant part of the method -is local to each process, and therefore can be accelerated on Graphics Processing Units (GPUs). The implementation of real-space preconditioning schemes [31,52] can further reduce the number of Self Consistent Field iterations for DFT simulations of large metallic systems. Finally, the incorporation of coarse-graining strategies [42,43] will further reduce the scaling to sublinear with the number of atoms.…”

“…Further, the number of SCF iterations to achieve a fixed target SCF error increases with system size in metallic systems due to charge sloshing [26]. The introduction of real space preconditioning schemes [52,31] is likely to reduce this for large metallic systems.…”

“…In view of this, the wall time for an SCF iteration of 25,000 Mg atoms with a prismatic dislocation loop calculated using spectral quadrature on 2400 MPI ranks is 4 hours, which can significantly decrease with the use of accelerators such as Graphics Processing Unit for performing the matrix-vector products. The 25,000 Mg showed significant charge-sloshing, which can be mitigated by real-space preconditioning schemes [31,52].…”

Implementation of Perdew–Zunger self-interaction correction in real space using Fermi–Löwdin orbitals

“…89 The SCF method is accelerated using the restarted variant 90 of Periodic Pulay mixing 91 with real-space preconditioning. 92 For spin polarized calculations, mixing is performed simultaneously on both components.…”

M-SPARC: Matlab-Simulation Package for Ab-initio Real-space Calculations

“…For the very first electronic ground state calculation, the superposition of isolated atom electron densities is used as initial guess for the electron density, whereas for every subsequent such calculation, extrapolation based on previous solutions is used [31]. The convergence of the SCF iteration is accelerated using the restarted variant of the Periodic Pulay mixing scheme [32,33], with the option of real-space preconditioning [34]. For spin-polarized calculations, mixing is performed simultaneously for both spin components, i.e., using a vector of twice the original length containing both spin-up and…”