NUMERICAL METHODS FOR THE SOLUTION OF THE POISSON EQUATION

We consider here the solution of the most ubiquitous elliptic equations, the Poisson Equation. One method that will not be given consideration is FEM, the reason being that time constraints will not permit us to do so. We'll consider instead

1)

FD methods $\left\{\begin{array}{l} \mbox {5-point}\\ \mbox {9-point}\end{array}\right\}$ for 2D problem

2)

Multigrid method $\rightarrow$ we'll cover only the basics

3)

Fast Poisson-Solvers.

We assume that students will have a background in direct and iterative methods for the solution of linear equations and working knowledge of the FFT (See FFT portion of Hw 8..