Jérôme Fehrenbach ; Mohamed Masmoudi - An introduction to the topological asymptotic expansion with examples

arima:1866 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, October 20, 2006, Volume 5, Special Issue TAM TAM'05, november 2006 - https://doi.org/10.46298/arima.1866
An introduction to the topological asymptotic expansion with examplesArticle

Authors: Jérôme Fehrenbach ORCID1; Mohamed Masmoudi 1

  • 1 Mathématiques pour l'Industrie et la Physique

To find an optimal domain is equivalent to look for Its characteristic function. At first sight this problem seems to be nondifferentiable. But it is possible to derive the variation of a cost function when we switch the characteristic function from 0 to 1 or from 1 to 0 a small area. Classical and two generalized adjoint approaches are considered in this paper. Their domain of validity is given and Illustrated by several examples. Using this gradient type Information, It is possible to build fast algorithms. Generally, only one Iteration Is needed to find the optimal shape.

https://doi.org/10.46298/arima.1866
Source: HAL:hal-01263433v1
Volume: Volume 5, Special Issue TAM TAM'05, november 2006
Published on: October 20, 2006
Submitted on: April 5, 2006
Keywords: Topological sensitivity, shape optimization, inverse problem, Lagrange operator, adjoint meth,Sensibilité topologique,optimisation de forme,problème inverse,opérateur de Lagrange,méthodes ajointes,[MATH]Mathematics [math],[INFO]Computer Science [cs]

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