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Pré-Publication, Document De Travail Année : 2018

Post-processing of the planewave approximation of Schrödinger equations. Part II: Kohn-Sham models

Résumé

In the first part of this article [6], we have presented a priori estimates for the perturbation-based post-processing of the plane-wave approximation of linear Schrödinger equations. In this article, we extend the proofs of such estimates in the nonlinear case of Kohn-Sham LDA models with pseudopotentials. As in [5], where these a priori results were announced and tested numerically, we use a periodic setting, and the problem is discretized with planewaves (Fourier series). This post-processing method consists of performing a full computation in a coarse planewave basis, and then to compute corrections based on first-order perturbation theory in a fine basis, which numerically only requires the computation of the residuals of the ground-state orbitals in the fine basis. We show that this procedure asymptotically improves the accuracy of two quantities of interest: the ground-state density matrix, i.e. the orthogonal projector on the lowest N eigenvectors, and the ground-state energy.
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Dates et versions

hal-01908044 , version 1 (29-10-2018)
hal-01908044 , version 2 (20-11-2018)
hal-01908044 , version 3 (17-03-2020)

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  • HAL Id : hal-01908044 , version 1

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Geneviève Dusson. Post-processing of the planewave approximation of Schrödinger equations. Part II: Kohn-Sham models. 2018. ⟨hal-01908044v1⟩
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