RESEARCH THE OCTA NT-BASED ALGORITHM FOR MESHLESS RBF-FD METHODS TO SOLVE THE POISSON EQUATION ON COMPLICATED 3D DOMAINS

Abstract

The algorithm of the octant-based stencil selection for the Radial Basis Function -Finite Difference (RBFFD) method for solving the Poisson equations in 3D was introduced by Oleg Davydov, Thi Oanh Dang, and Manh Tuong Ngo (2020). This algorithm is very effective for testing problems on geometrical domains which are cubes or spheres. In this paper, we presents an algorithm improved from the algorithm of the octant-based stencil selection for the problem on complicated geometric domains. The numerical experiments showed that the approximate solution of the RBF-FD method using the improved algorithm had higher stability and accuracy than the approximation solution of FEM and the published results.