Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals
DOI10.4208/nmtma.OA-2022-0026MaRDI QIDQ5885720
Aihui Zhou, Xiaoying Dai, Li-wei Zhang
Publication date: 4 April 2023
Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2111.02779
convergencedensity functional theorytemporal discretizationgradient flow based modelorthogonality preserving scheme
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Computational methods for invariant manifolds of dynamical systems (37M21)
Cites Work
- Unnamed Item
- Unnamed Item
- Finite element method for solving Kohn-Sham equations based on self-adaptive tetrahedral mesh
- A spectrum theorem for perturbed bounded linear operators
- Numerical analysis of finite dimensional approximations of Kohn-Sham models
- A parallel orbital-updating based optimization method for electronic structure calculations
- A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
- Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models
- Elliptic Preconditioner for Accelerating the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory
- Gradient Type Optimization Methods For Electronic Structure Calculations
- On the Convergence of the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory
- An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
- A Trust Region Direct Constrained Minimization Algorithm for the Kohn–Sham Equation
- Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure
- On the Convergence of the Self-Consistent Field Iteration for a Class of Nonlinear Eigenvalue Problems
- The Geometry of Algorithms with Orthogonality Constraints
- A Conjugate Gradient Method for Electronic Structure Calculations
- A New First-Order Algorithmic Framework for Optimization Problems with Orthogonality Constraints
- Gradient Flow Based Kohn--Sham Density Functional Theory Model
- An Implicit Solver for the Time-Dependent Kohn-Sham Equation
- Numerical Methods for Electronic Structure Calculations of Materials
- Numerical methods for Kohn–Sham density functional theory
- Parallelizable Algorithms for Optimization Problems with Orthogonality Constraints
- Adaptive Finite Element Approximations for Kohn--Sham Models
- A Riemannian Newton Algorithm for Nonlinear Eigenvalue Problems
- On the Analysis of the Discretized Kohn--Sham Density Functional Theory
- Electronic Structure
- Iterative Procedures for Nonlinear Integral Equations
- Convergence Analysis of Direct Minimization and Self-Consistent Iterations
This page was built for publication: Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals