15 citations · 69 across the 23 of their papers we have counts for
23 papers
An Augmented Subspace Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations
Xiaoying Dai, Miao Hu, Jack Xin +1
In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. By augmen…
Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems
Xiaoying Dai, Stefano de Gironcoli, Bin Yang +1
In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a gene…
Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals
Xiaoying Dai, Liwei Zhang, Aihui Zhou
To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose…
Layer-splitting methods for time-dependent Schrödinger equations of incommensurate systems
Ting Wang, Huajie Chen, Aihui Zhou +1
This work considers numerical methods for the time-dependent Schrödinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensu…
A plane wave study on the localized-extended transitions in the one-dimensional incommensurate systems
Huajie Chen, Aihui Zhou, Yuzhi Zhou
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of pote…
Pactical Newton Methods for Electronic Structure Calculations
Xiaoying Dai, Liwei Zhang, Aihui Zhou
In this paper, we propose and analyze some practical Newton methods for electronic structure calculations. We show the convergence and the local quadratic convergence rate for the…
Gradient Flow Based Discretized Kohn-Sham Density Functional Theory
Xiaoying Dai, Qiao Wang, Aihui Zhou
In this paper, we propose and analyze a gradient flow based Kohn-Sham density functional theory. First, we prove that the critical point of the gradient flow based model can be a l…
Two-Grid based Adaptive Proper Orthogonal Decomposition Algorithm for Time Dependent Partial Differential Equations
Xiaoying Dai, Xiong Kuang, Jack Xin +1
In this article, we propose a two-grid based adaptive proper orthogonal decomposition (POD) method to solve the time dependent partial differential equations. Based on the error ob…
Adaptive Step Size Strategy for Orthogonality Constrained Line Search Methods
Xiaoying Dai, Liwei Zhang, Aihui Zhou
In this paper, we propose an adaptive step size strategy for a class of line search methods for orthogonality constrained minimization problems, which avoids the classic backtracki…
Plane Wave Methods for Quantum Eigenvalue Problems of Incommensurate Systems
Yuzhi Zhou, Huajie Chen, Aihui Zhou
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximat…
A Mathematical Aspect of Hohenberg-Kohn Theorem
Aihui Zhou
The Hohenberg-Kohn theorem plays a fundamental role in density functional theory, which has become a basic tool for the study of electronic structure of matter. In this article, we…
A parallel orbital-updating based plane-wave basis method for electronic structure calculations
Yan Pan, Xiaoying Dai, Stefano de Gironcoli +3
Motivated by the recently proposed parallel orbital-updating approach in real space method, we propose a parallel orbital-updating based plane-wave basis method for electronic stru…
A conjugate gradient method for electronic structure calculations
Xiaoying Dai, Zhuang Liu, Liwei Zhang +1
In this paper, we study a conjugate gradient method for electronic structure calculations. We propose a Hessian based step size strategy, which together with three orthogonality ap…
A Parallel Orbital-updating Based Optimization Method for Electronic Structure Calculations
Xiaoying Dai, Zhuang Liu, Xin Zhang +1
In this paper, we propose a parallel optimization method for electronic structure calculations based on a single orbital-updating approximation. It is shown by our numerical experi…
A Parallel Orbital-Updating Approach for Electronic Structure Calculations
Xiaoying Dai, Xingao Gong, Aihui Zhou +1
In this paper, we propose an orbital iteration based parallel approach for electronic structure calculations. This approach is based on our understanding of the single-particle equ…
Gradient type optimization methods for electronic structure calculations
Xin Zhang, Jinwei Zhu, Zaiwen Wen +1
The density functional theory (DFT) in electronic structure calculations can be formulated as either a nonlinear eigenvalue or direct minimization problem. The most widely used app…
Adaptive Finite Element Approximations for Kohn-Sham Models
Huajie Chen, Xiaoying Dai, Xingao Gong +2
The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanoscien…
Convergence Rate and Quasi-Optimal Complexity of Adaptive Finite Element Computations for Multiple Eigenvalues
Xiaoying Dai, Lianhua He, Aihui Zhou
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation tec…
A Symmetry-based Decomposition Approach to Eigenvalue Problems: Formulation, Discretization, and Implementation
Jun Fang, Xingyu Gao, Aihui Zhou
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approa…
Hohenberg-Kohn Theorem for Coulomb Type Systems
Aihui Zhou
Density functional theory (DFT) has become a basic tool for the study of electronic structure of matter, in which the Hohenberg-Kohn theorem plays a fundamental role in the develop…
Numerical Analysis of Finite Dimensional Approximations of Kohn-Sham Models
Huajie Chen, Xingao Gong, Lianhua He +2
In this paper, we study finite dimensional approximations of Kohn-Sham models, which are widely used in electronic structure calculations. We prove the convergence of the finite di…
Convergence and Optimal Complexity of Adaptive Finite Element Methods
Lianhua He, Aihui Zhou
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric e…
Convergence of Adaptive Finite Element Approximations for Nonlinear Eigenvalue Problems
H. Chen, X. Gong, L. He +1
In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to…