Convergence of the Point Integral method for Poisson Equation on Point Cloud

Zuoqiang Shi Tsinghua University Jian Sun Tsinghua University

Information Theory Numerical Analysis and Scientific Computing mathscidoc:1709.19002

Research in the Mathematical Sciences, 4, (1), 2017
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 prop- erties. Recently, we proposed a novel numerical method, Point Integral method (PIM), to discretize the Laplace-Beltrami operator on point clouds [28]. 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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@inproceedings{zuoqiang2017convergence,
  title={Convergence of the Point Integral method for Poisson Equation on Point Cloud},
  author={Zuoqiang Shi, and Jian Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170925163805513586820},
  booktitle={Research in the Mathematical Sciences},
  volume={4},
  number={1},
  year={2017},
}
Zuoqiang Shi, and Jian Sun. Convergence of the Point Integral method for Poisson Equation on Point Cloud. 2017. Vol. 4. In Research in the Mathematical Sciences. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170925163805513586820.
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