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

Abstract

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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.

How to cite

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Morin, 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 -

References

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