A posteriori error estimation for the non-self-consistent Kohn-Sham equations
Computational Physics
2020-09-04 v2 Materials Science
Numerical Analysis
Numerical Analysis
Abstract
We address the problem of bounding rigorously the errors in the numerical solution of the Kohn-Sham equations due to (i) the finiteness of the basis set, (ii) the convergence thresholds in iterative procedures, (iii) the propagation of rounding errors in floating-point arithmetic. In this contribution, we compute fully-guaranteed bounds on the solution of the non-self-consistent equations in the pseudopotential approximation in a plane-wave basis set. We demonstrate our methodology by providing band structure diagrams of silicon annotated with error bars indicating the combined error.
Keywords
Cite
@article{arxiv.2004.13549,
title = {A posteriori error estimation for the non-self-consistent Kohn-Sham equations},
author = {Michael F. Herbst and Antoine Levitt and Eric Cancès},
journal= {arXiv preprint arXiv:2004.13549},
year = {2020}
}