The extended adjoint method

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 adj...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2013-01, Vol.47 (1), p.83-108
Main Authors: Larnier, Stanislas, Masmoudi, Mohamed
Format: Article
Language:English
Subjects:
49Q10
49Q12
74P10
74P15
Adjoint method
Adjoints
Approximation
Asymptotic expansions
Calculus of variations
Exact sciences and technology
Explicit knowledge
Mathematical analysis
Mathematical models
Mathematics
Optimization
Perturbation methods
Sciences and techniques of general use
Studies
Topology
topology optimization
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Summary: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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2012020