Research using the Wendland RBF for the RBF-FD method to solve the Poisson equation in 3D

Abstract

In recent years, the meshless finite difference method based on radial basis functions (RBF-FD) of solving partial differential equation in 3D has been studied by many scientists. To find the RBF-FD weight vector, the authors used the Power RBF interpolation, which does not depend on the shape parameter. This paper presents the research results of using Wendland RBF interpolation to find the weight vectors for the RBF-FD method to solve Poisson equations in 3D. The numerical experiments showed that the solution of the RBF-FD method using the Wendland function has good accuracy compared to the solution of the finite element method (FEM - Finite Element Method).