95 citations · 275 across the 50 of their papers we have counts for
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The weak Galerkin finite element method for the Steklov eigenvalue problem
Shusheng Li, Hehu Xie, Qilong Zhai
This paper introduces the application of the weak Galerkin (WG) finite element method to solve the Steklov eigenvalue problem, focusing on obtaining lower bounds of the eigenvalues…
A New Subspace Iteration Algorithm for Solving Generalized Eigenvalue Problems
Biyi Wang, Hengbin An, Hehu Xie +1
It is needed to solve generalized eigenvalue problems (GEP) in many applications, such as the numerical simulation of vibration analysis, quantum mechanics, electronic structure, e…
Solving High Dimensional Partial Differential Equations Using Tensor Type Discretization and Optimization Process
Yangfei Liao, Yifan Wang, Hehu Xie
In this paper, we propose a tensor type of discretization and optimization process for solving high dimensional partial differential equations. First, we design the tensor type of…
Tensor Neural Network and Its Numerical Integration
Yifan Wang, Pengzhan Jin, Hehu Xie
In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polyno…
An Efficient Adaptive Finite Element Method for Eigenvalue Problems
Qichen Hong, Hehu Xie, Fei Xu
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This met…
GCGE: A Package for Solving Large Scale Eigenvalue Problems by Parallel Block Damping Inverse Power Method
Yu Li, Zijing Wang, Hehu Xie
We propose an eigensolver and the corresponding package, GCGE, for solving large scale eigenvalue problems. This method is the combination of damping idea, subspace projection meth…
On the convergence to local limit of nonlocal models with approximated interaction neighborhoods
Qiang Du, Hehu Xie, Xiaobo Yin
Many nonlocal models have adopted Euclidean balls as the nonlocal interaction neighborhoods. When solving them numerically, it is sometimes convenient to adopt polygonal approximat…
Enhanced Error Estimates for Augmented Subspace Method
Haikun Dang, Yifan Wang, Hehu Xie +1
In this paper, some enhanced error estimates are derived for the augmented subspace methods which are designed for solving eigenvalue problems. We will show that the augmented subs…
On accelerating a multilevel correction adaptive finite element method for Kohn-Sham equation
Guanghui Hu, Hehu Xie, Fei Xu
Based on the numerical method proposed in [G. Hu, X. Xie, F. Xu, J. Comput. Phys., 355 (2018), 436-449.] for Kohn-Sham equation, further improvement on the efficiency is obtained i…
A Nonnested Augmented Subspace Method for Eigenvalue Problems with Curved Interfaces
Haikun Dang, Hehu Xie, Gang Zhao +1
In this paper, we present a nonnested augmented subspace algorithm and its multilevel correction method for solving eigenvalue problems with curved interfaces. The augmented subspa…
A Parallel Augmented Subspace Method for Eigenvalue Problems
Fei Xu, Hehu Xie, Ning Zhang
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, s…
Guaranteed eigenvalue bounds for the Steklov eigenvalue problem
Chun'guang You, Hehu Xie, Xuefeng Liu
To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is…
Fast eigenpairs computation with operator adapted wavelets and hierarchical subspace correction
Hehu Xie, Lei Zhang, Houman Owhadi
We present a method for the fast computation of the eigenpairs of a bijective positive symmetric linear operator . The method is based on a combination of operator ada…
Convergence Analysis of Shift-Inverse Method with Richardson Iteration For Eigenvalue Problem
Yunhui He, Hehu Xie
In this paper, we consider the shift-inverse method with Richardson iteration step for the eigenvalue problems. It will be shown that the convergence speed depends heavily on the e…
An Efficient Multigrid Method for Ground State Solution of Bose-Einstein Condensates
Hehu Xie, Fei Xu, Ning Zhang
An efficient multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the combination of the multigrid…
Acceleration of weak Galerkin methods for the Laplacian eigenvalue problem
Qilong Zhai, Hehu Xie, Ran Zhang +1
Recently, we proposed a weak Galerkin finite element method for the Laplace eigenvalue problem. In this paper, we present two-grid and two-space skills to accelerate the weak Galer…
Energy Error Estimates of Subspace Method and Multigrid Algorithm for Eigenvalue Problems
Yunhui He, Qichen Hong, Hehu Xie +2
This paper is to give a new understanding and applications of the subspace projection method for selfadjoint eigenvalue problems. A new error estimate in the energy norm, which is…
A Full Multigrid Method For Semilinear Elliptic Equation
Hehu Xie, Fei Xu
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solution…
A Small Note About Lower Bound of Eigenvalues
Hehu Xie, Chunguang You
This paper gives a framework to produce the lower bound of eigenvalues defined in a Hilbert space by the eigenvalues defined in another Hilbert space. The method is based on using…
Computable Error Estimates for Ground State Solution of Bose-Einstein Condensates
Hehu Xie, Manting Xie
In this paper, we propose a computable error estimate of the Gross-Pitaevskii equation for ground state solution of Bose-Einstein condensates by general conforming finite element m…
A Multigrid Method for the Ground State Solution of Bose-Einstein Condensates Based on Newton Iteration
Hehu Xie, Fei Xu, Meiling Yue
In this paper, a new kind of multigrid method is proposed for the ground state solution of Bose-Einstein condensates based on Newton iteration method. Instead of treating eigenvalu…
Anisotropic meshes and stabilized parameters for the stabilized finite element methods
Yana Di, Hehu Xie, Xiaobo Yin
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convecti…
Fully Computable Error Bounds for Eigenvalue Problem
Hehu Xie, Meiling Yue, Ning Zhang
This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based…
A Multilevel Correction Method for Interior Transmission Eigenvalue Problem
Hehu Xie, Xinming Wu
In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the tr…