THE RBF-FD METHOD TO SOLVE THE POISSON EQUATION IN 3D WITH THE K-NEAREST POINTS

Abstract

In recent years, the meshless finite difference method based on radial basis functions (RBF-FD) of solving partial differential equation has been studied by many scientists. However, the research results of this method are limited in 2D. This paper presents results of a new method, using the selection of k-nearest points to be a set of centers, which supports the RBF-FD method to solve Poisson's equation in 3D. The numerical experiments showed that the solution of the RBF-FD method using k-nearest points has higher accuracy than the solution of the finite element method.