The Frequency Decomposition Multilevel Method: A robust additive hierarchical basis preconditioner
Abstract: Hackbusch's frequency decomposition multilevel 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 semicoarsening, which demands fewer 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.
Affiliation: Department of Mathematics, Nijmegen University, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
Keywords: Frequency decomposition, multilevel method, semicoarsening, finite elements, hierarchical basis, additive Schwarz method, subspace decomposition, robustness
Received by editor(s): August 1, 1994
Article copyright: © Copyright 1996 American Mathematical Society