185 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- University of Electronic Science and Technology of ChinaCN23 papers
- Sichuan UniversityCN18 papers
- University of Hong KongHK11 papers
- London School of Economics and Political ScienceGB9 papers
- Southwest Jiaotong UniversityCN9 papers
- University of GroningenNL8 papers
- Hong Kong Polytechnic UniversityHK6 papers
- The University of MelbourneAU6 papers
- University of PittsburghUS6 papers
- Chengdu UniversityCN5 papers
- Chinese Academy of SciencesCN5 papers
- Hong Kong University of Science and TechnologyHK5 papers
34 papers · 1 filter
Approximating and preconditioning the stiffness matrix in the GoFD approximation of the fractional Laplacian
Weizhang Huang, Jinye Shen
In the finite difference approximation of the fractional Laplacian the stiffness matrix is typically dense and needs to be approximated numerically. The effect of the accuracy in a…
A moving mesh finite element method for Bernoulli free boundary problems
Jinye Shen, Heng Dai, Weizhang Huang
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a…
Meshfree finite difference solution of homogeneous Dirichlet problems of the fractional Laplacian
Jinye Shen, Bowen Shi, Weizhang Huang
A so-called grid-overlay finite difference method (GoFD) was proposed recently for the numerical solution of homogeneous Dirichlet boundary value problems of the fractional Laplaci…
A grid-overlay finite difference method for the fractional Laplacian on arbitrary bounded domains
Weizhang Huang, Jinye Shen
A grid-overlay finite difference method is proposed for the numerical approximation of the fractional Laplacian on arbitrary bounded domains. The method uses an unstructured simpli…
Regularized Barzilai-Borwein method
Congpei An, Xin Xu
We develop a novel stepsize based on \BB method for solving some challenging optimization problems efficiently, named regularized \BB (RBB) stepsize. We indicate that RBB stepsize…
An adaptive low-rank splitting approach for the extended Fisher--Kolmogorov equation
Yong-Liang Zhao, Xian-Ming Gu
The extended Fisher--Kolmogorov (EFK) equation has been used to describe some phenomena in physical, material and biology systems. In this paper, we propose a full-rank splitting s…
On the quadrature exactness in hyperinterpolation
Congpei An, Hao-Ning Wu
This paper investigates the role of quadrature exactness in the approximation scheme of hyperinterpolation. Constructing a hyperinterpolant of degree requires a positive-weight…
The springback penalty for robust signal recovery
Congpei An, Hao-Ning Wu, Xiaoming Yuan
We propose a new penalty, the springback penalty, for constructing models to recover an unknown signal from incomplete and inaccurate measurements. Mathematically, the springback p…
On the bilateral preconditioning for an L2-type all-at-once system arising from time-space fractional Bloch-Torrey equations
Yong-Liang Zhao, Xian-Ming Gu, Hu Li
Time-space fractional Bloch-Torrey equations (TSFBTEs) are developed by some researchers to investigate the relationship between diffusion and fractional-order dynamics. In this pa…
An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation
Yong-Liang Zhao, Meng Li, Alexander Ostermann +1
The space fractional Cahn-Hilliard phase-field model is more adequate and accurate in the description of the formation and phase change mechanism than the classical Cahn-Hilliard m…
A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations
Yong-Liang Zhao, Alexander Ostermann, Xian-Ming Gu
Fractional Ginzburg-Landau equations as the generalization of the classical one have been used to describe various physical phenomena. In this paper, we propose a numerical integra…
Tikhonov regularization for polynomial approximation problems in Gauss quadrature points
Congpei An, Hao-Ning Wu
This paper is concerned with the introduction of Tikhonov regularization into least squares approximation scheme on by orthonormal polynomials, in order to handle noisy da…
A preconditioning technique for an all-at-once system from Volterra subdiffusion equations with graded time steps
Yong-Liang Zhao, Xian-Ming Gu, Alexander Ostermann
Volterra subdiffusion problems with weakly singular kernel describe the dynamics of subdiffusion processes well.The graded scheme is often chosen to discretize such problems s…
Fast second-order implicit difference schemes for time distributed-order and Riesz space fractional diffusion-wave equations
Huan-Yan Jian, Ting-Zhu Huang, Xian-Ming Gu +2
In this paper, fast numerical methods are established for solving a class of time distributed-order and Riesz space fractional diffusion-wave equations. We derive new difference sc…
A note on parallel preconditioning for the all-at-once solution of Riesz fractional diffusion equations
Xian-Ming Gu, Yong-Liang Zhao, Xi-Le Zhao +2
The -step backwards difference formula (BDF) for solving the system of ODEs can result in a kind of all-at-once linear systems, which are solved via the parallel-in-time precond…
Fast implicit difference schemes for time-space fractional diffusion equations with the integral fractional Laplacian
Xian-Ming Gu, Hai-Wei Sun, Yanzhi Zhang +1
In this paper, we develop two fast implicit difference schemes for solving a class of variable-coefficient time-space fractional diffusion equations with integral fractional Laplac…
An energy-based discontinuous Galerkin method for semilinear wave equations
Daniel Appelo, Thomas Hagstrom, Qi Wang +1
We generalize the energy-based discontinuous Galerkin method proposed in [SIAM J. Num. Anal., 53(6):2705-2726, 2015.] to second-order semilinear wave equations. A stability and con…
A fast implicit difference scheme for solving the generalized time-space fractional diffusion equations with variable coefficients
Xian-Ming Gu, Ting-Zhu Huang, Yong-Liang Zhao +2
In this paper, we first propose an unconditionally stable implicit difference scheme for solving generalized time-space fractional diffusion equations (GTSFDEs) with variable coeff…
Randomized algorithms for the low multilinear rank approximations of tensors
Maolin Che, Yimin Wei, Hong Yan
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular va…
A Hessenberg-type Algorithm for Computing PageRank Problems
Xian-Ming Gu, Siu-Long Lei, Ke Zhang +3
PageRank is a widespread model for analysing the relative relevance of nodes within large graphs arising in several applications. In the current paper, we present a cost-effective…
Fast Cadzow's Algorithm and a Gradient Variant
Haifeng Wang, Jian-Feng Cai, Tianming Wang +1
The Cadzow's algorithm is a signal denoising and recovery method which was designed for signals corresponding to low rank Hankel matrices. In this paper we first introduce a Fast C…
An implicit integration factor method for a kind of spatial fractional diffusion equations
Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu +2
A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order…
An efficient second-order convergent scheme for one-side space fractional diffusion equations with variable coefficients
Xue-lei Lin, Pin Lyu, Michael K. Ng +2
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing sch…
A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation
Pin Lyu, Yuxiang Liang, Zhibo Wang
In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discret…