On Round-off Error for Adaptive Finite Element Methods

Handle URI:
http://hdl.handle.net/10754/552450
Title:
On Round-off Error for Adaptive Finite Element Methods
Authors:
Alvarez-Aramberri, J.; Pardo, David; Paszynski, Maciej; Collier, Nathan; Dalcin, Lisandro ( 0000-0001-8086-0155 ) ; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called ‘radical meshes’. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
On Round-off Error for Adaptive Finite Element Methods 2012, 9:1474 Procedia Computer Science
Journal:
Procedia Computer Science
Conference/Event name:
12th Annual International Conference on Computational Science, ICCS 2012
Issue Date:
2-Jun-2012
DOI:
10.1016/j.procs.2012.04.162
Type:
Conference Paper
ISSN:
18770509
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S1877050912002839
Appears in Collections:
Conference Papers; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAlvarez-Aramberri, J.en
dc.contributor.authorPardo, Daviden
dc.contributor.authorPaszynski, Maciejen
dc.contributor.authorCollier, Nathanen
dc.contributor.authorDalcin, Lisandroen
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-05-07T13:46:38Zen
dc.date.available2015-05-07T13:46:38Zen
dc.date.issued2012-06-02en
dc.identifier.citationOn Round-off Error for Adaptive Finite Element Methods 2012, 9:1474 Procedia Computer Scienceen
dc.identifier.issn18770509en
dc.identifier.doi10.1016/j.procs.2012.04.162en
dc.identifier.urihttp://hdl.handle.net/10754/552450en
dc.description.abstractRound-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called ‘radical meshes’. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.en
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S1877050912002839en
dc.rightsArchived with thanks to Procedia Computer Science. http://creativecommons.org/licenses/by-nc-nd/3.0/en
dc.subjectFinite Element Methods (FEM)en
dc.subjecthp-adaptivityen
dc.subjectround-off erroren
dc.subjectcondition numberen
dc.titleOn Round-off Error for Adaptive Finite Element Methodsen
dc.typeConference Paperen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalProcedia Computer Scienceen
dc.conference.date2012-06-04 to 2012-06-06en
dc.conference.name12th Annual International Conference on Computational Science, ICCS 2012en
dc.conference.locationOmaha, NB, USAen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionCONICET, Santa Fe, Argentinaen
dc.contributor.institutionAGH University of Science and Technology, Krakow, Polanden
dc.contributor.institutionIkerbasque, Bilbao, Spainen
dc.contributor.institutionDepartment of Applied Mathematics, Statistics, and Operational Research, University of the Basque Country UPV/EHU, Bilbao, Spainen
kaust.authorCollier, Nathaniel Orenen
kaust.authorCalo, Victor M.en
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