MathSciDoc: An Archive for Mathematician ∫

 
Log In
Sign Up
Help
Go
 

A convergent point integral method for isotropic elliptic equations on point cloud

Zhen Li Tsinghua University Zuoqiang Shi Tsinghua University

Numerical Analysis and Scientific Computing mathscidoc:1709.25006

SIAM: Multiscale Modeling & Simulation , 14, (2), 874-905, 2016
In this paper, we propose a numerical method to solve isotropic elliptic equations on point cloud by generalizing the point integral method. The idea of the point integral method is to approximate the differential operators by integral operators and discretize the corresponding integral equation on point cloud. The key step is to get the integral approximation. In this paper, with proper kernel function, we get an integral approximation for the elliptic operators with isotropic coefficients. Moreover, the integral approximation has been proved to keep the coercivity of the original elliptic operator. The convergence of the point integral method is also proved.
Point integral method; point cloud; isotropic elliptic operator; convergence analysis
[ Download ] [ 2017-09-27 09:41:09 uploaded by shizqi ] [ 594 downloads ] [ 0 comments ] 
@inproceedings{zhen2016a,
  title={A CONVERGENT POINT INTEGRAL METHOD FOR ISOTROPIC ELLIPTIC EQUATIONS ON POINT CLOUD},
  author={Zhen Li, and Zuoqiang Shi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170927094110049826825},
  booktitle={SIAM: Multiscale Modeling & Simulation },
  volume={14},
  number={2},
  pages={874-905},
  year={2016},
}
Zhen Li, and Zuoqiang Shi. A CONVERGENT POINT INTEGRAL METHOD FOR ISOTROPIC ELLIPTIC EQUATIONS ON POINT CLOUD. 2016. Vol. 14. In SIAM: Multiscale Modeling & Simulation . pp.874-905. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170927094110049826825.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved