# Full Multigrid convergence is too slow. What could possibly be causing it?

I've coded full multigrid in Matlab and it doesn't seem to be converging fast enough. When I increase the number of grids or the number of iterations, it converges to the analytical solution. But FMG shouldn't need that many iterations and it should work even for fewer grids.

I realize this is a very vague question, but are there any ideas why this may be?

• It would be useful if you stated what you think is "too slow". What convergence factors do you observe? Commented Jan 5, 2013 at 4:38
• @WolfgangBangerth Well I'm pretty sure (by my testing of a standard v-cycle), that I shouldn't need to run 30 iterations of FMG at 6 grids to get it to converge. It just doesn't make sense that such a versatile method should take that long. What do you mean by convergence factors? Commented Jan 6, 2013 at 1:25
• The convergence factor is the ratio of errors (or residuals) between successive iterations. For multigrid, typical convergence factors are 0.1-0.5. If it were, say, 0.1, then you'd need 6 iterations to reduce the error by a factor of $10^6$. If it were 0.5, you'd need 30 iterations to reduce it by a factor of $10^9$. Commented Jan 6, 2013 at 1:42

3. Check that two-grid convergence factors match the predictions from local Fourier analysis. (Use a problem with an analytic solution, or even solve $A x = 0$ with initial guess $x \ne 0$.)