Solution Of Two Dimensional Poisson Equation Using Finite Difference Method (Fdm) With Uniform And Non-Uniform Mesh Size. - Genet Mekonnen (My University, 2017)
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.