Block-triangular preconditioners for PDE-constrained optimization

Handle URI:
http://hdl.handle.net/10754/597687
Title:
Block-triangular preconditioners for PDE-constrained optimization
Authors:
Rees, Tyrone; Stoll, Martin
Abstract:
In this paper we investigate the possibility of using a block-triangular preconditioner for saddle point problems arising in PDE-constrained optimization. In particular, we focus on a conjugate gradient-type method introduced by Bramble and Pasciak that uses self-adjointness of the preconditioned system in a non-standard inner product. We show when the Chebyshev semi-iteration is used as a preconditioner for the relevant matrix blocks involving the finite element mass matrix that the main drawback of the Bramble-Pasciak method-the appropriate scaling of the preconditioners-is easily overcome. We present an eigenvalue analysis for the block-triangular preconditioners that gives convergence bounds in the non-standard inner product and illustrates their competitiveness on a number of computed examples. Copyright © 2010 John Wiley & Sons, Ltd.
Citation:
Rees T, Stoll M (2010) Block-triangular preconditioners for PDE-constrained optimization. Numerical Linear Algebra with Applications 17: 977–996. Available: http://dx.doi.org/10.1002/nla.693.
Publisher:
Wiley-Blackwell
Journal:
Numerical Linear Algebra with Applications
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
26-Nov-2010
DOI:
10.1002/nla.693
Type:
Article
ISSN:
1070-5325
Sponsors:
Contract/grant sponsor: King Abdullah University of Science and Technology (KAUST); contract/grant number: KUK-C1-013-04
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorRees, Tyroneen
dc.contributor.authorStoll, Martinen
dc.date.accessioned2016-02-25T12:44:25Zen
dc.date.available2016-02-25T12:44:25Zen
dc.date.issued2010-11-26en
dc.identifier.citationRees T, Stoll M (2010) Block-triangular preconditioners for PDE-constrained optimization. Numerical Linear Algebra with Applications 17: 977–996. Available: http://dx.doi.org/10.1002/nla.693.en
dc.identifier.issn1070-5325en
dc.identifier.doi10.1002/nla.693en
dc.identifier.urihttp://hdl.handle.net/10754/597687en
dc.description.abstractIn this paper we investigate the possibility of using a block-triangular preconditioner for saddle point problems arising in PDE-constrained optimization. In particular, we focus on a conjugate gradient-type method introduced by Bramble and Pasciak that uses self-adjointness of the preconditioned system in a non-standard inner product. We show when the Chebyshev semi-iteration is used as a preconditioner for the relevant matrix blocks involving the finite element mass matrix that the main drawback of the Bramble-Pasciak method-the appropriate scaling of the preconditioners-is easily overcome. We present an eigenvalue analysis for the block-triangular preconditioners that gives convergence bounds in the non-standard inner product and illustrates their competitiveness on a number of computed examples. Copyright © 2010 John Wiley & Sons, Ltd.en
dc.description.sponsorshipContract/grant sponsor: King Abdullah University of Science and Technology (KAUST); contract/grant number: KUK-C1-013-04en
dc.publisherWiley-Blackwellen
dc.subjectKrylov subspacesen
dc.subjectLinear systemsen
dc.subjectPDE-constrained optimizationen
dc.subjectPreconditioningen
dc.subjectSaddle point problemsen
dc.titleBlock-triangular preconditioners for PDE-constrained optimizationen
dc.typeArticleen
dc.identifier.journalNumerical Linear Algebra with Applicationsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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