Efficient single-grid and multi-grid solvers for real-space orbital-free density functional theory

Abstract

To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved bisection method to accelerate the line search process in the outer iteration, and extended the single-grid solver to a multi-grid solver. Numerical examples show that while maintaining high level of accuracy, the proposed single-grid solver can improve the computational efficiencies by two orders of magnitude comparing with the methods in the literature (For example, the ground state energy of a 45×45×45 FCC Aluminum cluster (376786 atoms) can be computed within 4h27min on a desktop computer.) and the multi-grid solver can improve the computational efficiencies even once for the cases where high-resolution electron densities are needed.