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
Inria de Paris, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
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
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Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík. A perturbation-method-based post-processing for the planewave discretization of Kohn–Sham models. Journal of Computational Physics, Elsevier, 2016, 307, pp.446-459. ⟨10.1016/j.jcp.2015.12.012⟩. ⟨hal-01140818v2⟩

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