Convergence of the Point Integral method for Poisson equation on point cloud
Numerical Analysis
2016-05-05 v4 Differential Geometry
Spectral Theory
Abstract
The Laplace-Beltrami operator (LBO) is a fundamental object associated to Riemannian manifolds, which encodes all intrinsic geometry of the manifolds and has many desirable properties. Recently, we proposed a novel numerical method, Point Integral method (PIM), to discretize the Laplace-Beltrami operator on point clouds \cite{LSS}. In this paper, we analyze the convergence of Point Integral method (PIM) for Poisson equation with Neumann boundary condition on submanifolds isometrically embedded in Euclidean spaces.
Keywords
Cite
@article{arxiv.1403.2141,
title = {Convergence of the Point Integral method for Poisson equation on point cloud},
author = {Zuoqiang Shi and Jian Sun},
journal= {arXiv preprint arXiv:1403.2141},
year = {2016}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1312.4424