TY - JOUR
T1 - Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud
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 - <p style="text-align: justify;">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.</p>