I have a nicely working multigrid solver, which I use for solving the Poisson equation from an electrostatic problem. I solve this equation first without any charges, and then many times with a slowly changing charge distribution.
Right now, I do a FMG from scratch each time I solve this equation, ignoring the fact that I already have a previous solution which could be updated instead of starting new from scratch. But if I use a V- or a W-cycle for this, I fear that there might be situations (if the charge distribution changed significantly) where this is worse than just starting from scratch with FMG.
I could try to apply FMG to the difference between my old solution and the final solution. However, this might be wasteful (in terms of memory), because I would have to store both the old solution, the real right hand side, the right hand side for the difference, and the difference on the finest grid. Hence I wonder whether using the F-cycle instead wouldn't be just as good, or even equivalent to this procedure.