What's the situation with intelligent mesh generation: A survey and perspectives

N Lei, Z Li, Z Xu, Y Li, X Gu - IEEE transactions on visualization …, 2023 - ieeexplore.ieee.org
Intelligent Mesh Generation (IMG) represents a novel and promising field of research,
utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG …

The implicit closest point method for the numerical solution of partial differential equations on surfaces

CB Macdonald, SJ Ruuth - SIAM Journal on Scientific Computing, 2010 - SIAM
Many applications in the natural and applied sciences require the solutions of partial
differential equations (PDEs) on surfaces or more general manifolds. The closest point …

A physics-informed neural network framework for PDEs on 3D surfaces: Time independent problems

Z Fang, J Zhan - IEEE Access, 2019 - ieeexplore.ieee.org
Partial differential equations (PDEs) on surfaces are ubiquitous in all the nature science.
Many traditional mathematical methods has been developed to solve surfaces PDEs …

Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators

A Jiao, Q Yan, J Harlim, L Lu - arxiv preprint arxiv:2407.05477, 2024 - arxiv.org
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 …

The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

C Piret - Journal of Computational Physics, 2012 - Elsevier
Much work has been done on reconstructing arbitrary surfaces using the radial basis
function (RBF) method, but one can hardly find any work done on the use of RBFs to solve …

An RBF-FD closest point method for solving PDEs on surfaces

A Petras, L Ling, SJ Ruuth - Journal of Computational Physics, 2018 - Elsevier
Partial differential equations (PDEs) on surfaces appear in many applications throughout the
natural and applied sciences. The classical closest point method (Ruuth and Merriman …

A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces

A Petras, L Ling, C Piret, SJ Ruuth - Journal of Computational Physics, 2019 - Elsevier
The closest point method (Ruuth and Merriman (2008)[32]) is an embedding method
developed to solve a variety of partial differential equations (PDEs) on smooth surfaces …

[HTML][HTML] An AFC-stabilized implicit finite element method for partial differential equations on evolving-in-time surfaces

A Sokolov, R Ali, S Turek - Journal of Computational and Applied …, 2015 - Elsevier
In this article we present a new implicit numerical scheme for reaction–diffusion–advection
equations on an evolving in time hypersurface Γ (t). The partial differential equations are …

A Closest Point Method for PDEs on manifolds with interior boundary conditions for geometry processing

N King, H Su, M Aanjaneya, S Ruuth… - ACM Transactions on …, 2024 - dl.acm.org
Many geometry processing techniques require the solution of partial differential equations
(PDEs) on manifolds embedded in ℝ2 or ℝ3, such as curves or surfaces. Such manifold …

Generalized finite difference method on unknown manifolds

SW Jiang, R Li, Q Yan, J Harlim - Journal of Computational Physics, 2024 - Elsevier
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 …