Gaussian-Approximated Poisson Preconditioner for Iterative Diagonalization in Real-Space Density Functional Theory

Abstract

Various real-space methods optimized on massive parallel computers have been developed for efficient large-scale density functional theory (DFT) calculations of materials and biomolecules. The iterative diagonalization of the Hamiltonian matrix is a computational bottleneck in real-space DFT calculations. Despite the development of various iterative eigensolvers, the absence of efficient real-space preconditioners has hindered their overall efficiency. An efficient preconditioner must satisfy two conditions: appropriate acceleration of the convergence of the iterative process and inexpensive computation. This study proposed a Gaussian-approximated Poisson preconditioner (GAPP) that satisfied both conditions and was suitable for real-space methods. A low computational cost was realized through the Gaussian approximation of a Poisson Green's function. Fast convergence was achieved through the proper determination of Gaussian coefficients to fit the Coulomb energies. The performance of GAPP was evaluated for several molecular and extended systems, and it showed the highest efficiency among the existing preconditioners adopted in real-space codes.