Multigrid can be applied in different cycling strategies. The parameter mc in the multigrid algorithm determines the number of recursive calls of the coarser level processing. Typically it chosen as mc=1, as in the multigrid workbench, leading to so-called V-cycles.
Alternatively, mc=2 can be used, leading to so-called W-cycles.
W-cycles are usually more robust and they are easier to analyze in the classical multigrid convergence theory. However, they are more expensive, and in local refinement applications (or in 1D) they may fail to have optimal work count. W-cycles are especially expensive in parallel algorithms when frequent coarse grid visits lead to poor processor utilization.
Either V- or W-cycles can (and should be) used in full multigrid mode.
Besides a fixed cycling strategy, accommodative cycles may be used. The idea here is to monitor the progress of the iteration in some way and to decide adaptively whether to go to finer or coarser levels. This is especially useful, when used in a adaptive refinement setting, see Ref. 14. on this list of references.
Ulrich Ruede , Thu Feb 2 21:05:10 MEZ 1995
Updated by Craig C. Douglas