A Generalized FDM for solving the Poisson's Equation on 3D Irregular Domains

Abstract

In this paper a new method for solving the Poisson’s equation with Dirichlet conditions on irregular domains is presented. For this purpose a generalized finite differences method is applied for numerical differentiation on irregular meshes. Three examples on cylindrical and spherical domains are considered. The numerical results are compared with analytical solution. These results show the performance and efficiency of the proposed method.