Robustness of the additive and multiplicative frequency decomposition multi-level method
type: Item
instance of: scholarly article
title: Robustness of the additive and multiplicative frequency decomposition multi-level method
zbMATH Open document ID: 0824.65105
DOI: 10.1007/BF02238231
published in: Computing
publication date: 1995-11-13T00:00:00Z
review text: A multiplicative variant of the frequency decomposition multi-level method (FDMLM) developed earlier by W. Hackbusch is studied. The abstract finite element spaces and their subspaces decomposition that underlies the FDMLM are defined. The additive and multiplicative FDMLM are described as subspace correction methods. Robustness of both the methods applied to second-order symmetric singular perturbation problems is proven. Results of numerical experiments for a two-dimensional anisotropic equation and the Helmholtz equation are presented. They show that the additive FDMLM is superior to standard BPX for these problems. The BPX (Bramble-Pasciak-Xu) preconditioner is a parallel subspace correction method corresponding to the overlapping decomposition with one Jacobi iteration as a smoother.
reviewed by: Krassimir Georgiev
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 769257
zbMATH Keywords: multigrid method
zbMATH Keywords: domain decomposition
zbMATH Keywords: hierarchical basis
zbMATH Keywords: Bramble- Pasciak-Xu preconditioner
zbMATH Keywords: Jacobi iteration
zbMATH Keywords: frequency decomposition multi-level method
zbMATH Keywords: finite element
zbMATH Keywords: subspace correction methods
zbMATH Keywords: singular perturbation
zbMATH Keywords: numerical experiments
zbMATH Keywords: anisotropic equation
zbMATH Keywords: Helmholtz equation
author: Rob P. Stevenson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 769257