On the multigrid F-cycle

摘要

In a recent paper, a bound was derived on the convergence of the multigrid V-cycle for the case when the solution is in the Sobolev space H1+α but not in H1+α', α' #62;; α, showing that the convergence factor approaches one only as 1 − O(k(α-1)/α) for a large number of levels k. We now extend the technique to obtain the asymptotically better bound 1 − O(k-(1-α)2 / α) on the multigrid F-cycle. We also show that in many cases, for practical values of k, one gets the same bound for the F-cycle as for the V-cycle with α = 1.