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Workshop on Advances on Scientific and Engineering Computing (I)

Point Integral Method: A Novel Numerical Method for Poisson Equation on Point Cloud

Speaker

Zuoqiang Shi (史作强) , Tsinghua University

Time

27 Sep, 10:40 - 11:20

Abstract

Partial differential equations on manifolds have been widely studied and play a crucial role in many subjects. In this talk, we will present a novel numerical method, point integral method to solve elliptic equations on point cloud. This method is based on an nonlocal approximation of elliptic operators. Then the elliptic equation can be transfered to an integral equation which is easy to discretize on unstructured point cloud. We will also present a high order nonlocal approximation for Dirichlet problem.