Convergence of the Point Integral method for the Poisson equation with Dirichlet boundary on point cloud
arXiv:1312.442410 citationsh-index: 28
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Provides theoretical justification for a numerical method used in geometry processing and related fields.
The authors prove convergence of the Point Integral method for solving Poisson equations with Dirichlet boundary conditions on manifolds from point clouds.
The Poisson equation on manifolds plays an fundamental role in many applications. Recently, we proposed a novel numerical method called the Point Integral method (PIM) to solve the Poisson equations on manifolds from point clouds. In this paper, we prove the convergence of the point integral method for solving the Poisson equation with the Dirichlet boundary condition.