On the Analysis of the Discretized Kohn--Sham Density Functional Theory

DOI10.1137/140957962zbMath1317.15008arXiv1402.5052OpenAlexW1852068959MaRDI QIDQ5499974

Xiao Wang, ZaiWen Wen, Michael Ulbrich, Xin Liu, Ya-Xiang Yuan

Publication date: 5 August 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.5052

zbMATH Keywords

nonlinear eigenvalue problemKohn-Sham equationKohn-Sham total energy minimizationself-consistent field iteration

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Nonlinear programming (90C30) Eigenvalues, singular values, and eigenvectors (15A18) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10)

Related Items (22)

Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals ⋮ An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory ⋮ Implicit algorithms for eigenvector nonlinearities ⋮ A parallel orbital-updating based optimization method for electronic structure calculations ⋮ Transportless conjugate gradient for optimization on Stiefel manifold ⋮ The space decomposition method for the sum of nonlinear convex maximum eigenvalues and its applications ⋮ A Conjugate Gradient Method for Electronic Structure Calculations ⋮ Variational Characterization of Monotone Nonlinear Eigenvector Problems and Geometry of Self-Consistent Field Iteration ⋮ A brief introduction to manifold optimization ⋮ Efficient Numerical Methods for Computing the Stationary States of Phase Field Crystal Models ⋮ Gradient Flow Based Kohn--Sham Density Functional Theory Model ⋮ A Riemannian conjugate gradient method for optimization on the Stiefel manifold ⋮ Perturbation analysis of an eigenvector-dependent nonlinear eigenvalue problem with applications ⋮ Projection-Based Embedding Theory for Solving Kohn--Sham Density Functional Theory ⋮ A density matrix approach to the convergence of the self-consistent field iteration ⋮ Parallelizable Algorithms for Optimization Problems with Orthogonality Constraints ⋮ Global optimization with orthogonality constraints via stochastic diffusion on manifold ⋮ A Proximal Gradient Method for Ensemble Density Functional Theory ⋮ Convergence Analysis of Direct Minimization and Self-Consistent Iterations ⋮ Sharp Estimation of Convergence Rate for Self-Consistent Field Iteration to Solve Eigenvector-Dependent Nonlinear Eigenvalue Problems ⋮ Linearizable Eigenvector Nonlinearities ⋮ An Orthogonalization-Free Parallelizable Framework for All-Electron Calculations in Density Functional Theory

Uses Software

• Matlab
• KSSOLV

Cites Work

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