10 citations · 50 across the 21 of their papers we have counts for
22 papers
A model order reduction based adaptive parareal method for time-dependent partial differential equations
Xiaoying Dai, Miao Hu, Shuwei Shen
In this paper, we propose a model order reduction based adaptive parareal method for time-dependent partial differential equations. By using the data obtained by the fine propagato…
An orthogonality-preserving approach for eigenvalue problems
Tianyang Chu, Xiaoying Dai, Shengyue Wang +1
Solving large-scale eigenvalue problems poses a significant challenge due to the computational complexity and limitations on the parallel scalability of the orthogonalization opera…
A gradient flow model for the Gross--Pitaevskii problem: Mathematical and numerical analysis
Tianyang Chu, Xiaoying Dai, Jing Wu +1
This paper concerns the mathematical and numerical analysis of the normalized gradient flow model for the Gross--Pitaevskii eigenvalue problem, which has been widely used to…
Convergence of the adaptive finite element discretization based parallel orbital-updating method for eigenvalue problems
Xiaoying Dai, Yan Li, Bin Yang +1
It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finit…
Subspace method based on neural networks for eigenvalue problems
Xiaoying Dai, Yunying Fan, Zhiqiang Sheng
In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. We first construct a neural network-based orthogonal b…
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…
An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems
Xiaoying Dai, Aihui Zhou, Yuzhi Zhou
In this paper, we propose an extended plane wave framework to make the electronic structure calculations of the twisted bilayer 2D material systems practically feasible. Based on t…
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…
Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations
Xiaoying Dai, Yan Pan, Bin Yang +1
In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori…
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…
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…
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…
Stable parareal in time method for first and second order hyperbolic system
Xiaoying Dai, Yvon Maday
The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with…
Symmetric parareal algorithms for Hamiltonian systems
X. Dai, C. Le Bris, F. Legoll +1
The parareal in time algorithm allows to efficiently use parallel computing for the simulation of time-dependent problems. It is based on a decomposition of the time interval into…