6 papers
Divergence-free interpolation of tangential vector fields via matrix-valued kernels
Zhengjie Sun, Lishuo Dong, Biao Huang
We develop and analyze a family of divergence-free kernel interpolation methods for tangential vector fields on the unit sphere. Starting from scalar radial kernels in Euclidean sp…
Error estimates for vector field interpolation based on generalized matrix-valued kernels
Zhengjie Sun, Lishuo Dong, Leevan Ling
Matrix-valued kernels provide a flexible framework for approximating vector fields from scattered data, especially when structural constraints such as divergence-free or curl-free…
Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds
Zhengjie Sun, Leevan Ling
This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in and compact Riemannian manifolds. While inv…
Energy-conserving Kansa methods for Hamiltonian wave equations
Xiaobin Li, Meng Chen, Zhengjie Sun +2
We introduce a fast, constrained meshfree solver designed specifically to inherit energy conservation (EC) in second-order time-dependent Hamiltonian wave equations. For discretiza…
Learning PDEs from data on closed surfaces with sparse optimization
Zhengjie Sun, Leevan Ling, Ran Zhang
The discovery of underlying surface partial differential equation (PDE) from observational data has significant implications across various fields, bridging the gap between theory…
Structure-preserving Kernel-based methods for solving dissipative PDEs on surfaces
Zhengjie Sun, Leevan Ling, Meng Chen
In this paper, we propose a general meshless structure-preserving Galerkin method for solving dissipative PDEs on surfaces. By posing the PDE in the variational formulation and sim…