3 papers
math.NA2026
ND-TNN: Tensor-Neural-Network Approximation for High-Dimensional Nonlocal Diffusion Models
Ziyue Cai, Zuoqiang Shi
We study a numerical method, built on the tensor neural network (TNN) architecture introduced in \cite{wang2022tensor}, for solving nonlocal diffusion models in high-dimensional sp…
math.AP2026
A Nonlocal -Laplacian Interface Model with Sharp Interface
Kehan Shi, Zuoqiang Shi, Tangjun Wang
We propose an energy-based nonlocal -Laplacian interface problem. Neumann interface conditions are naturally formulated via the energy, while Dirichlet conditions are enforced t…
math.NA2024
On the implementation of linear finite element method for nonlocal diffusion model over 2D domain
Zuoqiang Shi
We propose an implementation of linear finite element method for nonlocal diffusion problem in 2D space. In the implementation, we reduce the integral from 4D to 2D which would sim…