An adaptive planewave method for electronic structure calculations

TL;DR

This paper introduces an adaptive planewave method that efficiently controls errors in eigenvalue problems for electronic structure calculations, reducing computational costs especially in nonlinear cases.

Contribution

It develops an adaptive approach combining convergence rates and error estimates to optimize planewave energy cut-offs for both linear and nonlinear eigenvalue problems.

Findings

Efficient error control for linear eigenvalue problems.

Reduced computational cost in nonlinear eigenvalue problems.

Successful application to Kohn-Sham DFT simulations.

Abstract

We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy cut-off for planewave discretizations, for both linear and nonlinear eigenvalue problems. The method is error controllable for linear eigenvalue problems in the sense that for a given required accuracy, an energy cut-off for which the solution matches the target accuracy can be reached efficiently. Further, the method is particularly promising for nonlinear eigenvalue problems in electronic structure calculations as it shall reduce the cost of early iterations in self-consistent algorithms. We present some numerical experiments for both linear and nonlinear eigenvalue problems. In particular, we provide electronic structure calculations for some insulator and metallic systems simulated with Kohn--Sham density functional theory (DFT) and the projector augmented wave (PAW) method, illustrating the efficiency and potential of the algorithm.