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

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.

arXiv admin note: substantial text overlap with arXiv:1312.4424

References in corpus (2)

• Consistency of spectral clustering
• Point Integral Method for Solving Poisson-type Equations on Manifolds from Point Clouds with Convergence Guarantees

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