Point integral method for elliptic equations with variable coefficients on point cloud

Zhen Li Tsinghua University Zuoqiang Shi Tsinghua University Jian Sun Tsinghua University

Numerical Analysis and Scientific Computing mathscidoc:1708.25001

In this paper, we generalize the point integral method to solve the general elliptic PDEs with variable coefficients and corresponding eigenvalue problems with Neumann, Robin and Dirichlet boundary conditions on point cloud. The main idea is using integral equations to approximate the original PDEs. The integral equations are easy to discretize on the point cloud. The truncation error of the integral approximation is analyzed. Numerical examples are presented to demonstrate that PIM is an effective method to solve the elliptic PDEs with smooth coefficients on point cloud.
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@inproceedings{zhenpoint,
  title={Point integral method for elliptic equations with variable coefficients on point cloud},
  author={Zhen Li, Zuoqiang Shi, and Jian Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170808171915754515807},
}
Zhen Li, Zuoqiang Shi, and Jian Sun. Point integral method for elliptic equations with variable coefficients on point cloud. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170808171915754515807.
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