Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud (Communications in Computational Physics, 2019)
In this paper, we generalize the point integral method to solve the generalelliptic PDEs with variable coefficients and corresponding eigenvalue problems withNeumann, Robin and Dirichlet boundary conditions on point cloud. The main ideais using integral equations to approximate the original PDEs. The integral equationsare 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 aneffective method to solve the elliptic PDEs with smooth coefficients on point cloud.