Handle URI:
http://hdl.handle.net/10754/597454
Title:
Adaptive finite element method for shape optimization
Authors:
Morin, Pedro; Nochetto, Ricardo H.; Pauletti, Miguel S.; Verani, Marco
Abstract:
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Citation:
Morin P, Nochetto RH, Pauletti MS, Verani M (2012) Adaptive finite element method for shape optimization. ESAIM: Control, Optimisation and Calculus of Variations 18: 1122–1149. Available: http://dx.doi.org/10.1051/cocv/2011192.
Publisher:
EDP Sciences
Journal:
ESAIM: Control, Optimisation and Calculus of Variations
Issue Date:
16-Jan-2012
DOI:
10.1051/cocv/2011192
Type:
Article
ISSN:
1292-8119; 1262-3377
Sponsors:
Partially supported by UNL through GRANT CAI+D 062-312, by CONICET through Grant PIP 112-200801-02182, by MinCyT of Argentina through Grant PICT 2008-0622 and by Argentina-Italy bilateral project "Innovative numerical methods for industrial problems with complex and mobile geometries".Partially supported by NSF grants DMS-0505454 and DMS-0807811, and by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).Partially supported by Italian MIUR PRIN 2008 "Analisi e sviluppo di metodi numerici avanzati per EDP" and by Argentina-Italy bilateral project "Innovative numerical methods for industrial problems with complex and mobile geometries".
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMorin, Pedroen
dc.contributor.authorNochetto, Ricardo H.en
dc.contributor.authorPauletti, Miguel S.en
dc.contributor.authorVerani, Marcoen
dc.date.accessioned2016-02-25T12:33:34Zen
dc.date.available2016-02-25T12:33:34Zen
dc.date.issued2012-01-16en
dc.identifier.citationMorin P, Nochetto RH, Pauletti MS, Verani M (2012) Adaptive finite element method for shape optimization. ESAIM: Control, Optimisation and Calculus of Variations 18: 1122–1149. Available: http://dx.doi.org/10.1051/cocv/2011192.en
dc.identifier.issn1292-8119en
dc.identifier.issn1262-3377en
dc.identifier.doi10.1051/cocv/2011192en
dc.identifier.urihttp://hdl.handle.net/10754/597454en
dc.description.abstractWe examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.en
dc.description.sponsorshipPartially supported by UNL through GRANT CAI+D 062-312, by CONICET through Grant PIP 112-200801-02182, by MinCyT of Argentina through Grant PICT 2008-0622 and by Argentina-Italy bilateral project "Innovative numerical methods for industrial problems with complex and mobile geometries".Partially supported by NSF grants DMS-0505454 and DMS-0807811, and by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).Partially supported by Italian MIUR PRIN 2008 "Analisi e sviluppo di metodi numerici avanzati per EDP" and by Argentina-Italy bilateral project "Innovative numerical methods for industrial problems with complex and mobile geometries".en
dc.publisherEDP Sciencesen
dc.subjectAdaptivityen
dc.subjectMesh refinement/coarseningen
dc.subjectShape optimizationen
dc.subjectSmoothingen
dc.titleAdaptive finite element method for shape optimizationen
dc.typeArticleen
dc.identifier.journalESAIM: Control, Optimisation and Calculus of Variationsen
dc.contributor.institutionConsejo Nacional de Investigaciones Cientificas y Tecnicas, Buenos Aires, Argentinaen
dc.contributor.institutionUniversity of Maryland, College Park, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionPolitecnico di Milano, Milan, Italyen
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