A meshfree point collocation method for elliptic interface problems

We present a meshfree generalized finite difference method for solving Poisson's equation with diffusion coefficient that contains jump discontinuities up to several orders of magnitude. To discretize the operator, we formulate strong form uses smearing discontinuity; and conservative formulation based on locally computed Voronoi cells. Additionally, propose novel enforcing Neumann boundary conditions is compatible operator. Finally, introduce way switch from obtain positivity preserving scheme. The presented numerical methods are benchmarked against four test cases varying complexity magnitude point clouds nodes not aligned discontinuity. Our results show new hybrid switches between two formulations produces better than classical approach high jumps in diffusivity.