Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization

Handle URI:
http://hdl.handle.net/10754/598100
Title:
Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization
Authors:
Heister, Timo; Rapin, Gerd
Abstract:
Efficient preconditioning for Oseen-type problems is an active research topic. We present a novel approach leveraging stabilization for inf-sup stable discretizations. The Grad-Div stabilization shares the algebraic properties with an augmented Lagrangian-type term. Both simplify the approximation of the Schur complement, especially in the convection-dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov-type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. © 2012 John Wiley & Sons, Ltd.
Citation:
Heister T, Rapin G (2012) Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization. Int J Numer Meth Fluids 71: 118–134. Available: http://dx.doi.org/10.1002/fld.3654.
Publisher:
Wiley-Blackwell
Journal:
International Journal for Numerical Methods in Fluids
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
29-Jan-2012
DOI:
10.1002/fld.3654
Type:
Article
ISSN:
0271-2091
Sponsors:
The majority of the research was done while both authors worked at the University of Gottingen, Germany. Timo Heister was partially supported by the German Research Foundation (DFG) through the Research Training Group GK 1023. This publication is based, in part, on the work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorHeister, Timoen
dc.contributor.authorRapin, Gerden
dc.date.accessioned2016-02-25T13:12:41Zen
dc.date.available2016-02-25T13:12:41Zen
dc.date.issued2012-01-29en
dc.identifier.citationHeister T, Rapin G (2012) Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization. Int J Numer Meth Fluids 71: 118–134. Available: http://dx.doi.org/10.1002/fld.3654.en
dc.identifier.issn0271-2091en
dc.identifier.doi10.1002/fld.3654en
dc.identifier.urihttp://hdl.handle.net/10754/598100en
dc.description.abstractEfficient preconditioning for Oseen-type problems is an active research topic. We present a novel approach leveraging stabilization for inf-sup stable discretizations. The Grad-Div stabilization shares the algebraic properties with an augmented Lagrangian-type term. Both simplify the approximation of the Schur complement, especially in the convection-dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov-type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. © 2012 John Wiley & Sons, Ltd.en
dc.description.sponsorshipThe majority of the research was done while both authors worked at the University of Gottingen, Germany. Timo Heister was partially supported by the German Research Foundation (DFG) through the Research Training Group GK 1023. This publication is based, in part, on the work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.subjectAugmented Lagrangianen
dc.subjectGrad-Div stabilizationen
dc.subjectNavier-Stokesen
dc.subjectOseen problemen
dc.subjectPreconditioningen
dc.subjectSchur complementen
dc.titleEfficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilizationen
dc.typeArticleen
dc.identifier.journalInternational Journal for Numerical Methods in Fluidsen
dc.contributor.institutionDepartment of Mathematics; Texas A&M University, College Station; TX; 77843-3368; USAen
dc.contributor.institutionInterior Engineering; Volkswagen AG; Wolfsburg; Germanyen
kaust.grant.numberKUS-C1-016-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.