Adaptive finite element method for shape optimization

Type
Article

Authors
Morin, Pedro
Nochetto, Ricardo H.
Pauletti, Miguel S.
Verani, Marco

Online Publication Date
2012-01-16

Print Publication Date
2012-10

Date
2012-01-16

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.

Acknowledgements
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".

Publisher
EDP Sciences

Journal
ESAIM: Control, Optimisation and Calculus of Variations

DOI
10.1051/cocv/2011192

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