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

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• 作者：Eric Cancè ; s^a ; ^{cances@cermics.enpc.fr" class="auth_mail" title="E-mail the corresponding author} ; Geneviè ; ve Dusson^b ; ^c ; ^{dusson@ann.jussieu.fr" class="auth_mail" title="E-mail the corresponding author} ; Yvon Maday^b ; ^d ; ^e ; ^{maday@ann.jussieu.fr" class="auth_mail" title="E-mail the corresponding author} ; Benjamin Stamm^b ; ^{stamm@ann.jussieu.fr" class="auth_mail" title="E-mail the corresponding author} ; Martin Vohralí ; k^f ; ^{martin.vohralik@inria.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Density-functional theory ; Perturbation method ; Planewave approximation ; Nonlinear eigenvalue problem ; Post-processing
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：307
• 期：Complete
• 页码：446-459
• 全文大小：692 K

文摘

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.