Moving Least Square Interpolation in Matrix-Based Finite Difference Schemes on Adaptive Cartesian Grids

A variety of applications related to engineering and physics can be mathematically modeled by Partial Differential Equations, such as Poisson's equation with Dirichlet or Neumann boundary conditions. This study focuses on the application of Moving Least Squares (MLS) interpolation within matrix-based Finite Difference schemes to approximate the two-dimensional Poisson's equation on adaptive Cartesian grids or Adaptive Mesh Refinement  in specific regions using Matlab. Communication between cells at different refinement levels is typically done using Lagrange interpolation methods; however, this paper investigates and discusses the benefits of MLS interpolation on the proposed approach.