# The extended adjoint method

Stanislas Larnier; Mohamed Masmoudi

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

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

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topLarnier, Stanislas, and Masmoudi, Mohamed. "The extended adjoint method." ESAIM: Mathematical Modelling and Numerical Analysis 47.1 (2012): 83-108. <http://eudml.org/doc/222128>.

@article{Larnier2012,

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},

keywords = {Adjoint method; topology optimization; calculus of variations; adjoint method},

language = {eng},

month = {7},

number = {1},

pages = {83-108},

publisher = {EDP Sciences},

title = {The extended adjoint method},

url = {http://eudml.org/doc/222128},

volume = {47},

year = {2012},

}

TY - JOUR

AU - Larnier, Stanislas

AU - Masmoudi, Mohamed

TI - The extended adjoint method

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2012/7//

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; adjoint method

UR - http://eudml.org/doc/222128

ER -

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