A black-box multigrid preconditioner for the biharmonic equation
type: Item
instance of: scholarly article
title: A black-box multigrid preconditioner for the biharmonic equation
zbMATH Open document ID: 1053.65092
author: David Silvester
author: M. D. Mihajlović
published in: BIT
publication date: 2004-08-06T00:00:00Z
review text: Mixed finite element discretizations of biharmonic equations lead to saddle point systems. The paper considers a conventional and a constraint block preconditioner for such systems. The condition numbers of the preconditioned systems are studied. Numerical tests with the exact and two inexact versions of the constraint block preconditioner are presented. The inexact versions approximate a discrete Laplacian by a number of multigrid V-cycles. The iteration number of a preconditioned BICGSTAB(2) method tends to grow slowly with mesh refinement, \(O(h^{-1/2})\), for the exact version and in the case that sufficiently many multigrid cycles are applied in the inexact version.
reviewed by: Volker John
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 2081534
zbMATH Keywords: biharmonic equation
zbMATH Keywords: mixed finite element
zbMATH Keywords: preconditioning
zbMATH Keywords: comparison of methods
zbMATH Keywords: Laplace equation
zbMATH Keywords: numerical examples
zbMATH Keywords: saddle point systems
zbMATH Keywords: condition numbers
zbMATH Keywords: multigrid V-cycles
zbMATH Keywords: mesh refinement
MaRDI profile type: Publication
DOI: 10.1023/B:BITN.0000025094.68655.C7
description: scientific article; zbMATH DE number 2081534