DC FieldValueLanguage
dc.contributor.authorBörm, Steffen-
dc.contributor.authorLe Borne, Sabine-
dc.date.accessioned2020-02-18T13:57:06Z-
dc.date.available2020-02-18T13:57:06Z-
dc.date.issued2010-12-09-
dc.identifier.citationInternational Journal for Numerical Methods in Fluids 1 (68): 83-98 (2010)de_DE
dc.identifier.issn1097-0363de_DE
dc.identifier.urihttp://hdl.handle.net/11420/4963-
dc.description.abstractThe (mixed finite element) discretization of the linearized Navier-Stokes equations leads to a linear system of equations of saddle point type. The iterative solution of this linear system requires the construction of suitable preconditioners, especially in the case of high Reynolds numbers. In the past, a stabilizing approach has been suggested which does not change the exact solution but influences the accuracy of the discrete solution as well as the effectiveness of iterative solvers. This stabilization technique can be performed on the continuous side before the discretization, where it is known as 'grad-div' (GD) stabilization, as well as on the discrete side where it is known as an 'augmented Lagrangian' (AL) technique (and does not change the discrete solution). In this paper, we study the applicability of ℋ-LU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. We consider both the saddle point systems that arise from the stabilization in the continuous as well as on the discrete setting. Recently, a modified AL preconditioner has been proposed for the system resulting from the discrete stabilization. We provide a straightforward generalization of this approach to the GD stabilization. We conclude the paper with numerical tests for a variety of problems to illustrate the behavior of the considered preconditioners as well as the suitability of ℋ-LU factorization in the preconditioners.en
dc.language.isoende_DE
dc.publisherWileyde_DE
dc.relation.ispartofInternational journal for numerical methods in fluidsde_DE
dc.subjectℋ-LUde_DE
dc.subjectaugmented lagrangian methodde_DE
dc.subjectgrad-div stabilizationde_DE
dc.subjecthierarchical matricesde_DE
dc.subjectoseen problemde_DE
dc.subjectsaddle point problemsde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleℋ-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systemsde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishThe (mixed finite element) discretization of the linearized Navier-Stokes equations leads to a linear system of equations of saddle point type. The iterative solution of this linear system requires the construction of suitable preconditioners, especially in the case of high Reynolds numbers. In the past, a stabilizing approach has been suggested which does not change the exact solution but influences the accuracy of the discrete solution as well as the effectiveness of iterative solvers. This stabilization technique can be performed on the continuous side before the discretization, where it is known as 'grad-div' (GD) stabilization, as well as on the discrete side where it is known as an 'augmented Lagrangian' (AL) technique (and does not change the discrete solution). In this paper, we study the applicability of ℋ-LU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. We consider both the saddle point systems that arise from the stabilization in the continuous as well as on the discrete setting. Recently, a modified AL preconditioner has been proposed for the system resulting from the discrete stabilization. We provide a straightforward generalization of this approach to the GD stabilization. We conclude the paper with numerical tests for a variety of problems to illustrate the behavior of the considered preconditioners as well as the suitability of ℋ-LU factorization in the preconditioners.de_DE
tuhh.publisher.doi10.1002/fld.2495-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue1de_DE
tuhh.container.volume68de_DE
tuhh.container.startpage83de_DE
tuhh.container.endpage98de_DE
local.status.inpressfalsede_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorGNDBörm, Steffen-
item.creatorGNDLe Borne, Sabine-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidBörm, Steffen-
item.creatorOrcidLe Borne, Sabine-
item.languageiso639-1en-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0002-4399-4442-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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