Elliptic preconditioner for accelerating the self consistent field iteration in Kohn-Sham density functional theory

TL;DR

This paper introduces an elliptic preconditioner for Kohn-Sham density functional theory that accelerates self-consistent field iterations, especially effective for large inhomogeneous systems at low temperature.

Contribution

A novel elliptic preconditioner is proposed, unifying treatment for insulating and metallic systems, improving convergence rates in large-scale DFT calculations.

Findings

More effective than existing methods for large inhomogeneous systems

Keeps convergence rate independent of system size

Works well for both insulating and metallic systems

Abstract

We discuss techniques for accelerating the self consistent field (SCF) iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point map satisfied by the total potential. They can be viewed as preconditioners for a fixed point iteration. We point out different requirements for constructing preconditioners for insulating and metallic systems respectively, and discuss how to construct preconditioners to keep the convergence rate of the fixed point iteration independent of the size of the atomistic system. We propose a new preconditioner that can treat insulating and metallic system in a unified way. The new preconditioner, which we call an elliptic preconditioner, is constructed by solving an elliptic partial differential equation. The elliptic preconditioner is shown to be more effective in accelerating the convergence of a fixed point iteration than the existing approaches for large inhomogeneous systems at low temperature.