Modified Virtual Grid Difference for Discretizing the Laplace--Beltrami Operator on Point Clouds
Modified Virtual Grid Difference for Discretizing the Laplace--Beltrami Operator on Point Clouds
We propose a new and simple discretization, named the modified virtual grid difference (MVGD), for numerical approximation of the Laplace--Beltrami (LB) operator on manifolds sampled by point clouds. The key observation is that both the manifold and a function defined on it can both be parametrized in a local Cartesian …