8 citations · 15 across the 6 of their papers we have counts for
6 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…
Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators
Anran Jiao, Qile Yan, Jhn Harlim +1
In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown…
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…
Kernel-based methods for Solving Time-Dependent Advection-Diffusion Equations on Manifolds
Qile Yan, Shixiao Willing Jiang, John Harlim
In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM) and ghost point diffusion maps (GPDM), to solve the time-dependent advection-diffusion PDE o…