3 papers
math.NA2026
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…
math.NA2025
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…
math.NA2025
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…