Point Integral Method for Solving Poisson-Type Equations on Manifolds from Point Clouds with Convergence Guarantees

DOI10.4208/cicp.111015.250716azbMath1488.65714arXiv1409.2623OpenAlexW2963561100MaRDI QIDQ5159054

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Publication date: 26 October 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.2623

zbMATH Keywords

convergenceLaplace-Beltrami operatorpoint cloudpoint integral method

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Numerical methods for integral equations (65R20) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) PDEs on manifolds (35R01)

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Uses Software

• CGAL

Cites Work

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• Data analysis and representation on a general domain using eigenfunctions of Laplacian
• Quantum mechanics on manifolds embedded in Euclidean space.
• A simple embedding method for solving partial differential equations on surfaces
• Scale selection properties of generalized scale-space interest point detectors
• Solving Partial Differential Equations on Point Clouds
• Stability of Delaunay-type structures for manifolds
• The Implicit Closest Point Method for the Numerical Solution of Partial Differential Equations on Surfaces
• Spectral convergence of the connection Laplacian from random samples
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Calculus on Surfaces with General Closest Point Functions
• Integral estimation from point cloud in d-dimensional space
• Learning Theory
• Learning Theory
• Variational problems and partial differential equations on implicit surfaces

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