The frequency decomposition multilevel method: A robust additive hierarchical basis preconditioner

Hackbusch's frequency decomposition multi-level method is characterized by the application of three additional coarse-grid corrections in parallel to the standard one. Each coarse-grid correction was designed to damp errors from a different part of the frequency spectrum. In this paper, we introduce a cheap variant of this method, partly based on semi-coarsening, which demands less recursive calls than the original version. Using the theory of the additive Schwarz methods, we will prove robustness of our method as a preconditioner applied to anisotropic equations.