3 citations · 7 across the 4 of their papers we have counts for
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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…
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…