Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing |
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Authors: | Petr Vaněk Marian Brezina |
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Institution: | 1. Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14, Plzeň, Czech Republic 2. Department of Applied Mathematics, University of Colorado at Boulder, Campus Box 526, Boulder, CO, 80309-0526, USA
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Abstract: | 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 k, at least Ch k+1/h k , we prove a convergence result independent of h k+1/h k . 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 of our smoother is completely algebraic and independent of geometry of the problem and prolongators (the geometry of coarse spaces). |
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