Gaussian Elimination Solution to the 2D Poisson Equation

[Hypatio]

I am trying to use Gaussian elimination to solve the 2D poisson equation. I've done this for the 1D problem without problems, but for some reason my solution for the 2D problem is incorrect; it looks something like the correct solution but it's as if the resulting field were cut in half, so along the top boundary it looks like the solution to the 1D problem.

On slide 7 of some persons powerpoint presentation here,

http://www.ifi.uio.no/~infm3350/slides060904.pdf

there is a matrix A with some of the values =4 and others =-1, and this is the matrix I am trying to solve with the right side source term equal to 1. Is it somehow incorrect to directly apply gaussian elimination over this matrix as it is?

Also note that I do not fully und erstand what the second matrix is on that same slide represents or how to solve it, so if I actuallyneed this then I may be approaching the solution incorrectly.

Thanks.

 

[Hypatio]

I found the solution to my problem. Gaussian elimination can be applied without problems. My error was using a shortcut routine for back substitution for tridiagonal matrices which only work for the 1D poisson's problem.