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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