, Note that the choice of three pre-and three post-smoothing steps makes every iteration of the methods PCG(MG(3,3)-bJ) and MG(3,3)-GS considerably more expensive than those of the methods wRAS and MG-bGS with ? = 1, where the minimalist (0,1) choice is sufficient. The variants wRAS and MG-bGS with ? = 3 are also cheaper. In addition, in PCG(MG(3,3)-bJ), the coarse grid correction is more expensive as it uses order p approximations. The inversion of the Jacobi blocks in PCG(MG(3,3)-bJ) on the finest level J, corresponds to solving the patch problems of order p as in (3.8), so that its cost is the same as for the local problems of wRAS. As for MG(1,1)-PCG(iChol), we find the method to be quite satisfactory for lower-order approximations, but as soon as p and J increase, the number of iterations degrades considerably. In contrast to wRAS, MG-bGS is a multiplicative Schwarz method and is thus less suitable for parallelization. The classical MG(3,3)-GS is a combination of h-and p-multigrid and gives the best timings in our experiments. The numbers of preand post-smoothing steps, however, remain parameters, and their tuning might not be straightforward in order to get an efficient and numerically robust multigrid solver in general (cf. the poor results of the very similar, up to the different number of pre-and post-smoothing steps and a stronger hierarchy, The presented methods split into two groups: numerically p-robust (wRAS, PCG(MG-bJ), MG-bGS) and not (MG-PCG(iChol)

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