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Volume 26, Issue 2
Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud

Zhen Li, Zuoqiang Shi & Jian Sun

DOI: 10.4208/cicp.OA-2018-0024

Commun. Comput. Phys., 26 (2019), pp. 506-530.

Published online: 2019-04

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  • Abstract

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.

  • Keywords

Point integral method, elliptic equation, variable coefficients, point clouds.

  • AMS Subject Headings

65N12, 65N25, 65N75

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-506, author = {Zhen Li, Zuoqiang Shi and Jian Sun}, title = {Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {2}, pages = {506--530}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0024}, url = {http://global-sci.org/intro/article_detail/cicp/13100.html} }
TY - JOUR T1 - Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud AU - Zhen Li, Zuoqiang Shi & Jian Sun JO - Communications in Computational Physics VL - 2 SP - 506 EP - 530 PY - 2019 DA - 2019/04 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0024 UR - https://global-sci.org/intro/article_detail/cicp/13100.html KW - Point integral method, elliptic equation, variable coefficients, point clouds. AB -

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.

Zhen Li, Zuoqiang Shi and Jian Sun. (2019). Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud. Communications in Computational Physics. 26 (2). 506-530. doi:10.4208/cicp.OA-2018-0024
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