6 papers
A Regularization Based Computational Method for Quantum Incommensurate Problems
Zhenan Ding, Yan Li, Aihui Zhou +1
Quantum incommensurate systems have attracted widespread interest due to their unique physical properties. Related studies have made notable progress in recent years. To gain deepe…
Spectral Analysis of the Schrödinger Operator for the Incommensurate System
Yan Li, Yujian Song, Aihui Zhou
Many novel and unique physical phenomena in incommensurate systems can be illustrated and predicted using their spectral structure and electronic state distributions. However, the…
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…
Numerical Analysis of the Parallel Orbital-Updating Approach for Eigenvalue Problems
Xiaoying Dai, Yan Li, Bin Yang +1
The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to…
A Mathematical Aspect of Bloch's Theorem
Yan Li, Bin Yang, Aihui Zhou
In this paper, by studying a class of 1-D Sturm-Liouville problems with periodic coefficients, we show and classify the solutions of periodic Schrodinger equations in a multidimens…