109 citations · 443 across the 45 of their papers we have counts for
21 papers · 1 filter
A Geometric Local Parameterization Method for Generalized Hele-Shaw Free Boundary Problems with Source Terms
Zengyan Zhang, Wenrui Hao, John Harlim
We develop a meshfree numerical framework for Hele--Shaw free boundary problems with surface tension and source terms based on geometric local parameterization and boundary integra…
Geometric local parameterization for solving Hele-Shaw problems with surface tension
Zengyan Zhang, Wenrui Hao, John Harlim
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented…
A Higher Order Local Mesh Method for Approximating 1-Laplacians on Unknown Manifolds
John Wilson Peoples, John Harlim
We introduce a numerical method for approximating arbitrary differential operators on vector fields in the weak form given point cloud data sampled randomly from a dimensional…
Learning Coarse-Grained Dynamics on Graph
Yin Yu, John Harlim, Daning Huang +1
We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the G…
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…