Minimal Poisson 2D

Solves the 2D Poisson equation with Robin boundary conditions on a uniform grid where \(\Delta x=\Delta y = 1\).

\[ \nabla^2 u(x,y) = f(x,y) \]

with \(x\in[0,5], y\in[0,5]\), and

\[\begin{split} f(x,y) = \begin{cases} 100 & \text{ if y = 0} \\ 0 & \text{ otherwise } \end{cases} \end{split}\]

The boundary conditions are given by

\[ au + b\nabla u = g \]

with \(a=1\), \(b=0\), and \(g=0\). This corresponds to the call to robinBC2D of robinBC2D(k, m, 1, n, 1, 1, 0).