1 citations · 1 across the 12 of their papers we have counts for
12 papers
fTNN: a tensor neural network for fractional PDEs
Qingkui Ma, Hehu Xie, Xiaobo Yin
We develop the fTNN, a deterministic tensor neural network subspace method for problems involving the fractional Laplacian on bounded domains, taking the fractional Poisson equatio…
Quadrature-Enhanced Monte Carlo fPINN Method for High-Dimensional Fractional PDEs
Qingkui Ma, Hehu Xie, Xiaobo Yin
Fractional PDEs involving the fractional Laplacian on bounded domains are challenging because of hypersingular nonlocal kernels, exterior Dirichlet constraints, reduced boundary re…
Analysis of Convergence for the IPA-AC Method
Xiuzhu Yang, Xiaobo Yin
The Improved Partial Area-Analytical Calculation (IPA-AC) method represents a leading meshfree discretization strategy for peridynamic models, distinguished by its rigorous geometr…
Solving Time-Fractional Partial Integro-Differential Equations Using Tensor Neural Network
Zhongshuo Lin, Qingkui Ma, Hehu Xie +1
In this paper, we propose a novel machine learning method based on adaptive tensor neural network subspace to solve linear time-fractional diffusion-wave equations and nonlinear ti…
Error estimates of finite element methods for nonlocal problems using exact or approximated interaction neighborhoods
Qiang Du, Hehu Xie, Xiaobo Yin +1
We study the asymptotic error between the finite element solutions of nonlocal models with a bounded interaction neighborhood and the exact solution of the limiting local model. Th…
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…
Analysis of (shifted) piecewise quadratic polynomial collocation for nonlocal diffusion model
Minghua Chen, Jiankang Shi, Xiaobo Yin
The piecewise quadratic polynomial collocation is used to approximate the nonlocal model, which generally obtain the {\em nonsymmetric indefinite system} [Chen et al., IMA J. Numer…
A conforming DG method for linear nonlocal models with integrable kernels
Qiang Du, Xiaobo Yin
Numerical solution of nonlocal constrained value problems with integrable kernels are considered. These nonlocal problems arise in nonlocal mechanics and nonlocal diffusion. The st…
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…
Metric tensors for the interpolation error and its gradient in norm
Xiaobo Yin, Hehu Xie
A uniform strategy to derive metric tensors in two spatial dimension for interpolation errors and their gradients in norm is presented. It generates anisotropic adaptive mesh…
New metric tensors for anisotropic mesh generation
Xiaobo Yin, Hehu Xie
A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform on…
A posteriori error estimators suitable for moving finite element methods under anisotropic meshes
Xiaobo Yin, Hehu Xie
In this paper, we give a new type of a posteriori error estimators suitable for moving finite element methods under anisotropic meshes for general second-order elliptic problems. T…