國立清華大學 數學系

Abstract： In this talk, I will introduce a new numerical method for Poisson equation on point cloud. The main advantage of this method is that it does not need mesh, the equation is discretized over the point cloud directly which makes the method very efficient and very easy to implement. Moreover, this numerical approach also preserve the elliptic properties of the original Poisson equation. Based on this property, we can prove the convergence of this method. This method is also applicable on the eigenvalue problem of Laplace-Beltrami operator on manifold. And the convergence is also proved. Tea Time: 3:30pm, R707