Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing
We analyze a general multigrid method with aggressive coarsening and polynomial smoothing. We use a special polynomial smoother that originates in the context of the smoothed aggregation method. Assuming the degree of the smoothing polynomial is, on each level , at least , we prove a convergence result independent of . The suggested smoother is cheaper than the overlapping Schwarz method that allows to prove the same result. Moreover, unlike in the case of the overlapping Schwarz method, analysis...