For 1D elliptic equation discretized with finite differences : Does the red/black ordering method for Gauss-Seidel algorithm imposes to have an odd number of points if one wants periodic boundary conditions?
If $i = 0,...,n$, $n$ is even, then the update of $i=0$ (which is black, say) needs $i=1$ and $i=n-1$. But because $n$ is even, $n-1$ is black too, there seems to be a problem because black should only use red points and vice versa.
So does red-black ordering and periodic boundary imposes an odd number of points ?
Thanks for you answer.