High order RBF-FD approximations with application to a scattering problem

Abstract

A recently suggested technique for high order meshless approximations is described and analyzed in this paper. It involves constructing ordinary Radial Basis Function-generated finite difference approximations augmented with monomials up to a given order to ensure higher convergence rates. These approximations are used to solve the Poisson’s equation on an annulus to demonstrate the predicted convergence rates. The presented methodology is then applied to a scattering problem, which is described by a coupled system of two complex-valued PDEs on two domains, sharing a common boundary.