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

作者：Cances Eric; Dusson Genevieve^*; Maday Yvon; Stamm Benjamin; Vohralik Martin

来源：Journal of Computational Physics, 2016, 307: 446-459.

DOI：10.1016/j.jcp.2015.12.012

• Density-functional theory
• Perturbation method
• Planewave approximation
• Nonlinear eigenvalue problem
• Post-processing

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.

• 出版日期2016-2-15
• 单位INRIA