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

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.

References in corpus (5)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case
• Non-perturbative embedding of local defects in crystalline materials

Cited by in corpus (1)

• Stochastic Algorithms for Self-consistent Calculations of Electronic Structures