NumericalPossionEquation. The main task of this project is to solve the Anisotropic Poisson equation by transforming the original problem into a linear equation using discrete differential approximations. Different methods have been attempted solving the linear equation with massive size, including direct Gauss elimination and Preconditioning Conjugate Gradient (PCG) with V-Cycle preconditioner using either Symmetric Line Gauss-Seidel Iterative Method or Symmetric Point Gauss-Seidel Iterative Method as smoother. Other methods, such as ordinary Conjugate Gradient Methods are also attempted.