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?

  • $\begingroup$ What do you mean by "system size"? The size of the problem or the number of computational units that compute the solution in parallel? $\endgroup$ May 13 '17 at 9:14
  • $\begingroup$ The size of the problem. I.e. the number of unknowns. $\endgroup$
    – user20867
    May 15 '17 at 6:11

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