It is my understanding that the multigrid solution techniques are generally the preferable method to solve large Poisson problems. Now assume I have written a multigrid solver that is tailored to my special needs that actually works quite well, i.e. the residual norm decreases by a factor ~10 with every successive V-cycle.
How would I actually show/prove/test for textbook efficiency? Can optimal scalability only be shown for a fixed continuous problem that is discretized onto increasingly finer grids? If so, are there any special properties such a problem should have?