Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud

Point Integral Method for Elliptic Equations with Variable Coefficients on Point Cloud

Year:    2019

Communications in Computational Physics, Vol. 26 (2019), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2018-0024

Communications in Computational Physics, Vol. 26 (2019), Iss. 2 : pp. 506–530

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Point integral method elliptic equation variable coefficients point clouds.

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