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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2020

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

Résumé

In this article, we provide a priori estimates for a perturbation-based post-processing method of the plane-wave approximation of nonlinear Kohn–Sham LDA models with pseudopotentials, relying on [6] for the proofs of such estimates in the case of linear Schrödinger equations. 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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Geneviève Dusson. Post-processing of the planewave approximation of Schrödinger equations. Part II: Kohn-Sham models. IMA Journal of Numerical Analysis, 2020, 41 (4), pp.2456-2487. ⟨10.1093/imanum/draa052⟩. ⟨hal-01908044v3⟩
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