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arXiv · 1403.2141

Convergence of the Point Integral method for Poisson equation on point cloud

Zuoqiang Shi·Jian Sun
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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.

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Zuoqiang Shi, Jian Sun. 2016-05-04. Convergence of the Point Integral method for Poisson equation on point cloud. https://arxiv.org/abs/1403.2141

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