# Adaptive finite element method for shape optimization

Pedro Morin; Ricardo H. Nochetto; Miguel S. Pauletti; Marco Verani

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 4, page 1122-1149
- ISSN: 1292-8119

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topMorin, Pedro, et al. "Adaptive finite element method for shape optimization." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 1122-1149. <http://eudml.org/doc/272757>.

@article{Morin2012,

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.},

author = {Morin, Pedro, Nochetto, Ricardo H., Pauletti, Miguel S., Verani, Marco},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {shape optimization; adaptivity; mesh refinement/coarsening; smoothing},

language = {eng},

number = {4},

pages = {1122-1149},

publisher = {EDP-Sciences},

title = {Adaptive finite element method for shape optimization},

url = {http://eudml.org/doc/272757},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Morin, Pedro

AU - Nochetto, Ricardo H.

AU - Pauletti, Miguel S.

AU - Verani, Marco

TI - Adaptive finite element method for shape optimization

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2012

PB - EDP-Sciences

VL - 18

IS - 4

SP - 1122

EP - 1149

AB - 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.

LA - eng

KW - shape optimization; adaptivity; mesh refinement/coarsening; smoothing

UR - http://eudml.org/doc/272757

ER -

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