Aihui Zhou
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View article: A gradient flow model for the Gross--Pitaevskii problem: Mathematical and numerical analysis
A gradient flow model for the Gross--Pitaevskii problem: Mathematical and numerical analysis Open
This paper concerns the mathematical and numerical analysis of the $L^2$ normalized gradient flow model for the Gross--Pitaevskii eigenvalue problem, which has been widely used to design the numerical schemes for the computation of the gro…
View article: Convergence of the adaptive finite element discretization based parallel orbital-updating method for eigenvalue problems
Convergence of the adaptive finite element discretization based parallel orbital-updating method for eigenvalue problems Open
It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finite element discretization based parallel orbital-updating me…
View article: A quasi-Grassmannian gradient flow model for eigenvalue problems
A quasi-Grassmannian gradient flow model for eigenvalue problems Open
We propose a quasi-Grassmannian gradient flow model for eigenvalue problems of linear operators, aiming to efficiently address many eigenpairs. Our model inherently ensures asymptotic orthogonality: without the need for initial orthogonali…
View article: Numerical Analysis of the Parallel Orbital-Updating Approach for Eigenvalue Problems
Numerical Analysis of the Parallel Orbital-Updating Approach for Eigenvalue Problems Open
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 be efficient, for instance, in electronic structure calcul…
View article: An augmented subspace based adaptive proper orthogonal decomposition method for time dependent partial differential equations
An augmented subspace based adaptive proper orthogonal decomposition method for time dependent partial differential equations Open
View article: A Mathematical Aspect of Bloch's Theorem
A Mathematical Aspect of Bloch's Theorem Open
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 multidimensional case, which tells that not all the solutions are Bloc…
View article: A Fast, Performant, Secure Distributed Training Framework For Large Language Model
A Fast, Performant, Secure Distributed Training Framework For Large Language Model Open
The distributed (federated) LLM is an important method for co-training the domain-specific LLM using siloed data. However, maliciously stealing model parameters and data from the server or client side has become an urgent problem to be sol…
View article: Conversion of Bacterial Cellulose Wastewater into Green Detergent by Waste Biomass Co-Fermentation
Conversion of Bacterial Cellulose Wastewater into Green Detergent by Waste Biomass Co-Fermentation Open
View article: Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations
Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations Open
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 error estimator and prove both the upper and lower bounds. …
View article: Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials
Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials Open
In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave method for t…
View article: An Augmented Subspace Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations
An Augmented Subspace Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations Open
In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. By augmenting the POD subspace with some auxiliary modes, we obtain …
View article: Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals
Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals Open
To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations.In this paper, we propose and analyze a class of iteration schemes for the discretized…
View article: An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems
An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems Open
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 the foundation in [Y. Zhou, H. Chen, A. Zhou, J. Comput. Phy…
View article: Symmetrized two-scale finite element discretizations for partial differential equations with symmetric solutions
Symmetrized two-scale finite element discretizations for partial differential equations with symmetric solutions Open
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
View article: Convergence of the Planewave Approximations for Quantum Incommensurate Systems
Convergence of the Planewave Approximations for Quantum Incommensurate Systems Open
Incommensurate structures arise from stacking single layers of low-dimensional materials on top of one another with misalignment such as an in-plane twist in orientation. While these structures are of significant physical interest, they po…
View article: Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems
Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems Open
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 general smearing approach are involved. We study the invariance…
View article: Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals
Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals Open
To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose and analyze a class of iteration schemes for the discretize…
View article: Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations
Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations Open
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 error estimator and prove both the upper and lower bounds. …
View article: Convergence and Optimal Complexity of the Adaptive Planewave Method for Eigenvalue Computations.
Convergence and Optimal Complexity of the Adaptive Planewave Method for Eigenvalue Computations. Open
In this paper, we study an adaptive planewave method for multiple eigenvalues of second-order elliptic partial equations. Inspired by the technique for the adaptive finite element analysis, we prove that the adaptive planewave method has t…
View article: Layer-splitting methods for time-dependent Schrödinger equations of incommensurate systems
Layer-splitting methods for time-dependent Schrödinger equations of incommensurate systems Open
This work considers numerical methods for the time-dependent Schrödinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensurate problem is lifted to a higher dimension that results i…
View article: Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics
Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics Open
In this paper, we investigate a class of nonlinear eigenvalue problems resulting from quantum physics. We first prove that for any open set G , there exists an eigenfunction that cannot be a polynomial on G , which may be reviewed as a ref…
View article: S3ML: A Secure Serving System for Machine Learning Inference
S3ML: A Secure Serving System for Machine Learning Inference Open
We present S3ML, a secure serving system for machine learning inference in this paper. S3ML runs machine learning models in Intel SGX enclaves to protect users' privacy. S3ML designs a secure key management service to construct flexible pr…
View article: A plane wave study on the localized-extended transitions in the one-dimensional incommensurate systems
A plane wave study on the localized-extended transitions in the one-dimensional incommensurate systems Open
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 potentials, which are in close connection to many recent experi…
View article: Pactical Newton Methods for Electronic Structure Calculations
Pactical Newton Methods for Electronic Structure Calculations Open
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 Newton method when the Newton search directions are well-ob…
View article: First-principles investigation of monatomic gold wires under tension
First-principles investigation of monatomic gold wires under tension Open
View article: Gradient Flow Based Discretized Kohn-Sham Density Functional Theory
Gradient Flow Based Discretized Kohn-Sham Density Functional Theory Open
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 local minimizer of the Kohn-Sham total energy. Then we apply…
View article: Eigenfunction Behavior and Adaptive Finite Element Approximations of Nonlinear Eigenvalue Problems in Quantum Physics
Eigenfunction Behavior and Adaptive Finite Element Approximations of Nonlinear Eigenvalue Problems in Quantum Physics Open
In this paper, we investigate a class of nonlinear eigenvalue problems resulting from quantum physics. We first prove that the eigenfunction cannot be a polynomial on any open set, which may be reviewed as a refinement of the classic uniqu…
View article: Two-Grid based Adaptive Proper Orthogonal Decomposition Algorithm for Time Dependent Partial Differential Equations
Two-Grid based Adaptive Proper Orthogonal Decomposition Algorithm for Time Dependent Partial Differential Equations Open
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 obtained in the coarse grid, we propose an error indicator fo…
View article: Adaptive Step Size Strategy for Orthogonality Constrained Line Search Methods
Adaptive Step Size Strategy for Orthogonality Constrained Line Search Methods Open
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 backtracking procedure. We prove the convergence of the line search m…
View article: Plane wave methods for quantum eigenvalue problems of incommensurate systems
Plane wave methods for quantum eigenvalue problems of incommensurate systems Open