3 citations · 6 across the 4 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…