Meshfree Finite Difference Solution of Fractional Laplacian Boundary Value Problems on Arbitrary Domains

This work explores the feasibility of using the grid-overlay finite difference method (GoFD) with point clouds for the numerical solution of homogeneous Dirichlet problems of the fractional Laplacian. Two approaches are proposed to construct the transfer matrix from the point cloud to the uniform grid, one based on moving least squares fitting and the other based on Delaunay triangulation and piecewise linear interpolation.