A perturbation-method-based post-processing for the planewave discretization of Kohn–Sham models

Eric Cancès; Geneviève Dusson; Yvon Maday; Benjamin Stamm; Martin Vohralík

doi:10.1016/j.jcp.2015.12.012

A perturbation-method-based post-processing for the planewave discretization of Kohn–Sham models

Eric Cancès ^{1, 2} Geneviève Dusson ^{3, 4} Yvon Maday ^{5, 4} Benjamin Stamm ⁴ Martin Vohralík ⁶

1 MATHERIALS - MATHematics for MatERIALS

CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris

2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

3 ICS - Institut du Calcul et de la Simulation

4 LJLL - Laboratoire Jacques-Louis Lions

5 Brown University

6 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms

Inria de Paris

Abstract : In this article, we propose a post-processing of the planewave solution of the Kohn–Sham LDA model with pseudopotentials. This post-processing is based upon the fact that the exact solution can be interpreted as a perturbation of the approximate solution, allowing us to compute corrections for both the eigenfunctions and the eigenvalues of the problem in order to increase the accuracy. Indeed, this post-processing only requires the computation of the residual of the solution on a finer grid so that the additional computational cost is negligible compared to the initial cost of the planewave-based method needed to compute the approximate solution. Theoretical estimates certify an increased convergence rate in the asymptotic convergence range. Numerical results confirm the low computational cost of the post-processing and show that this procedure improves the energy accuracy of the solution even in the pre-asymptotic regime which comprises the target accuracy of practitioners.

Keywords : post-processing nonlinear eigenvalue problem density-functional theory perturbation method planewave approximation

Document type :

Journal articles

Domain :

Mathematics [math]

Chemical Sciences

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https://hal.sorbonne-universite.fr/hal-01140818
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