Direct solvers performance on h-adapted grids

Handle URI:
http://hdl.handle.net/10754/577267
Title:
Direct solvers performance on h-adapted grids
Authors:
Paszynski, Maciej; Pardo, David; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Direct solvers performance on h-adapted grids 2015, 70 (3):282 Computers & Mathematics with Applications
Publisher:
Elsevier BV
Journal:
Computers & Mathematics with Applications
Issue Date:
27-May-2015
DOI:
10.1016/j.camwa.2015.05.007
Type:
Article
ISSN:
08981221
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0898122115002187
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorPaszynski, Maciejen
dc.contributor.authorPardo, Daviden
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-09-14T11:27:41Zen
dc.date.available2015-09-14T11:27:41Zen
dc.date.issued2015-05-27en
dc.identifier.citationDirect solvers performance on h-adapted grids 2015, 70 (3):282 Computers & Mathematics with Applicationsen
dc.identifier.issn08981221en
dc.identifier.doi10.1016/j.camwa.2015.05.007en
dc.identifier.urihttp://hdl.handle.net/10754/577267en
dc.description.abstractWe analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.en
dc.language.isoenen
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0898122115002187en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computers & Mathematics with Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers & Mathematics with Applications, 27 May 2015. DOI: 10.1016/j.camwa.2015.05.007en
dc.subjectDirect solveren
dc.subjecth-version refinementen
dc.subjectFinite element methoden
dc.subjectSingularitiesen
dc.titleDirect solvers performance on h-adapted gridsen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalComputers & Mathematics with Applicationsen
dc.eprint.versionPost-printen
dc.contributor.institutionAGH University of Sciences and Technology, Krakow, Polanden
dc.contributor.institutionDepartment of Applied Mathematics, Statistics, and Operational Research at the University of the Basque Country (UPV/EHU), Bilbao, Spainen
dc.contributor.institutionBasque Center for Applied Mathematics (BCAM), Bilbao, Spainen
dc.contributor.institutionBasque Foundation for Science (IKERBASQUE), Bilbao, Spainen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorCalo, Victor M.en
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