Weight calculation and convergence analysis of polyharmonic spline (PHS) with polynomials for different stencils

Abstract

Recent developments in the field of the radial basis function-finite difference (RBF-FD) framework have been focused on conditionally positive definite polyharmonic splines (PHS). Within this context, our research focuses on deriving analytical weights for the RBF-FD+polynomials method within the framework of PHS. We provide convergence analyses for various stencils. To validate the accuracy of our derived formulations, we conduct a series of computational experiments across a range of test problems.