Solution Of Two Dimensional Poisson Equation Using Finite Difference Method (Fdm) With Uniform And Non-Uniform Mesh Size.

Abstract

In this study, we examined on the finite difference solution of two dimensional Poisson equation with uniform and non-uniform mesh size. The Poisson equation is a very powerful tool for modeling the behavior of electrostatic systems, but unfortunately may not be solved analytically for very simplified models. Consequently, numerical simulation must be utilized in order to model the behavior of complex geometries with practical value. Although there are several competing algorithm for achieving this goal, one of the simplest and more straightforward of these is called the finite difference method (FDM). Therefore, the two dimensional Poisson equation is discretazi with uniform and non-uniform mesh size using finite difference method for the comparison purpose. The numerical solution is elaborated with examples. And the result is compared in terms of efficiency. Eventually, the convergence, stability and consistence is determined for uniform and non uniform mesh size. More over, we examine the ways that the two dimensional Poisson equation can be approximated by finite difference over non-uniform meshes, the result is compared with the respective approximation obtained by finite difference on uniform meshes. As result we obtained that for randomly distributed grid point the finite difference method is very complex and not sufficiently converge to the exact solution where as for uniformly distributed grid point it converge to the exact solution.