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

TL;DR

This paper introduces new single-grid and multi-grid solvers for real-space orbital-free density functional theory, significantly enhancing computational efficiency by up to two orders of magnitude compared to existing methods.

Contribution

The work develops a novel single-grid solver with closed-form inner solutions and an improved bisection line search, extending it to a multi-grid solver for high-resolution density calculations.

Findings

Single-grid solver improves efficiency by 100x over previous methods.

Multi-grid solver further accelerates high-resolution density computations.

Numerical tests confirm substantial efficiency gains.

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 the proposed single-grid solver can improve the computational efficiencies by two orders of magnitude comparing with the methods in the literature and the multi-grid solver can improve the computational efficiencies even once for the cases where high-resolution electron densities are needed.