Enforce the Dirichlet boundary condition by volume constraint in Point Integral method

Zuoqiang Shi Tsinghua University

Information Theory Numerical Analysis and Scientific Computing mathscidoc:1709.19003

Commun. Math. Sci., 15, (6), 1743-1769, 2017
Poisson equation on point cloud with Dirichlet boundary condition plays important role in many problems. In this paper, we use the volume constraint proposed by Du et.al to handle the Dirichlet boundary condition in the point integral method for Poisson equation on point cloud. We prove that the solution given by volume constraint converges to the true solution as the point cloud converges to the underlying smooth manifold.
Point Integral Method; volume constraint; Dirichlet boundary; Laplace-Beltrami
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@inproceedings{zuoqiang2017enforce,
  title={Enforce the Dirichlet boundary condition by volume constraint in Point Integral method},
  author={Zuoqiang Shi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170925165122218055822},
  booktitle={Commun. Math. Sci.},
  volume={15},
  number={6},
  pages={1743-1769},
  year={2017},
}
Zuoqiang Shi. Enforce the Dirichlet boundary condition by volume constraint in Point Integral method. 2017. Vol. 15. In Commun. Math. Sci.. pp.1743-1769. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170925165122218055822.
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