ENFORCE THE DIRICHLET BOUNDARY CONDITION BY VOLUME CONSTRAINT IN POINT INTEGRAL METHOD

被引：8
|
作者：
Shi, Zuoqiang [1 ]
机构：
[1] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China
来源：
COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2017年 / 15卷 / 06期
关键词：
Point Integral Method; volume constraint; Dirichlet boundary; Laplace-Beltrami operator; Poisson equation; PARTIAL-DIFFERENTIAL-EQUATIONS; NONLOCAL DIFFUSION; LAPLACIAN;
D O I：
10.4310/CMS.2017.v15.n6.a12
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Poisson equation on point cloud with Dirichlet boundary condition plays important role in many problems. In this paper, we use the volume constraint proposed by Du et.al to handle the Dirichlet boundary condition in the point integral method for Poisson equation on point cloud. We prove that the solution given by volume constraint converges to the true solution as the point cloud converges to the underlying smooth manifold.
引用
收藏
页码：1743 / 1769
页数：27
相关论文
共 50 条
12345