The extended adjoint method

Stanislas Larnier; Mohamed Masmoudi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 1, page 83-108
  • ISSN: 0764-583X

Abstract

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Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need the fundamental solution of the problem; furthermore our approach allows to consider finite perturbations and not infinitesimal ones. This paper provides theoretical justifications in the linear case and presents some applications with topological perturbations, continuous perturbations and mesh perturbations. This proposed approach can also be used to update the solution of singularly perturbed problems.

How to cite

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Larnier, Stanislas, and Masmoudi, Mohamed. "The extended adjoint method." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.1 (2013): 83-108. <http://eudml.org/doc/273329>.

@article{Larnier2013,
abstract = {Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need the fundamental solution of the problem; furthermore our approach allows to consider finite perturbations and not infinitesimal ones. This paper provides theoretical justifications in the linear case and presents some applications with topological perturbations, continuous perturbations and mesh perturbations. This proposed approach can also be used to update the solution of singularly perturbed problems.},
author = {Larnier, Stanislas, Masmoudi, Mohamed},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {adjoint method; topology optimization; calculus of variations},
language = {eng},
number = {1},
pages = {83-108},
publisher = {EDP-Sciences},
title = {The extended adjoint method},
url = {http://eudml.org/doc/273329},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Larnier, Stanislas
AU - Masmoudi, Mohamed
TI - The extended adjoint method
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 1
SP - 83
EP - 108
AB - Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need the fundamental solution of the problem; furthermore our approach allows to consider finite perturbations and not infinitesimal ones. This paper provides theoretical justifications in the linear case and presents some applications with topological perturbations, continuous perturbations and mesh perturbations. This proposed approach can also be used to update the solution of singularly perturbed problems.
LA - eng
KW - adjoint method; topology optimization; calculus of variations
UR - http://eudml.org/doc/273329
ER -

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