64 citations · 126 across the 15 of their papers we have counts for
15 papers
RBF-Generated Finite Difference Method Coupled with Quadratic Programming for Solving PDEs on Surfaces with Derivative Boundary Conditions
Peng Chen, Shixiao Willing Jiang, Rongji Li +1
Derivative boundary conditions introduce challenges for mesh-free discretizations of PDEs on surfaces, especially when the domain is represented by randomly sampled point clouds. T…
Two-step Generalized RBF-Generated Finite Difference Method on Manifolds
Rongji Li, Haichuan Di, Shixiao Willing Jiang
Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in v…
Generalized Moving Least-Squares Methods for Solving Vector-valued PDEs on Unknown Manifolds
Rongji Li, Qile Yan, Shixiao W. Jiang
In this paper, we extend the Generalized Moving Least-Squares (GMLS) method in two different ways to solve the vector-valued PDEs on unknown smooth 2D manifolds without boundaries…
Generalized Finite Difference Method on unknown manifolds
Shixiao W. Jiang, Rongji Li, Qile Yan +1
In this paper, we extend the Generalized Finite Difference Method (GFDM) on unknown compact submanifolds of the Euclidean domain, identified by randomly sampled data that (almost s…
Spectral methods for solving elliptic PDEs on unknown manifolds
Qile Yan, Shixiao Jiang, John Harlim
In this paper, we propose a mesh-free numerical method for solving elliptic PDEs on unknown manifolds, identified with randomly sampled point cloud data. The PDE solver is formulat…
Radial basis approximation of tensor fields on manifolds: From operator estimation to manifold learning
John Harlim, Shixiao Willing Jiang, John Wilson Peoples
In this paper, we study the Radial Basis Function (RBF) approximation to differential operators on smooth tensor fields defined on closed Riemannian submanifolds of Euclidean space…