Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing.
The paper theoretically analyzes a general multigrid method in the case of the so called aggressive coarsening, i.e., with large differences between characteristic mesh sizes of two successive spaces within the multigrid hierarchy. The authors extend earlier theoretical results by weakening the approximation property and prove a ``nearly optimal convergence'' result independent of the coarsening ratio and linearly depending on the number of levels. Allowing worse approximation properties of the spaces requires to satisfy a stronger smoothing condition. A simple algorithm for the realisation of a suitable polynomial smoother based on Richardson iteration is described.
scientific article; zbMATH DE number 6221236