SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2011-2012
Jeudi 12 janvier 2012 :
Marc BONNET
(ENSTA)
Identification d'inclusions ou de fissures utilisant l'asymptotique petit-défaut de fonctions coût.
We present recent work on the application of small-defect asymptotics of cost functionals (topological sensitivity, higher-order expansions) to flaw identification, in the framework of linear elastodynamics and acoustics in either the frequency or the time domain. Topics addressed include inclusion or crack identification, asymptotics of energy cost functionals (known in solid mechanics as error in constitutive equation functionals), and partial justifications in limiting situations (identification of small obstacles, Born approximation). Assessments of the approach include experiments on simple configurations allowing semi-analytic treatments, and purely numerical computations on arbitrary 3D configurations. Our presentation includes results obtained with Cédric Bellis (currently postdoc at Columbia University), Bojan Guzina (professor, University of Minnesota) and Gabriel Delgado (PhD student, Ecole Polytechnique).
