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SUMMARY:Recent developments on topological derivative methods for qualitat
 ive inverse scattering
DTSTART:20170407T121500
DTEND:20170407T131500
DTSTAMP:20260407T021901Z
UID:f8cd6be0615ed3c1b928586efcd6e3a46eced3e51ae87d6ef0e8dd27
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Dr Marc BONNET\, POEMS (ENSTA\, CNRS\, INRIA\, Universit
 é Paris-Saclay)\, Palaiseau\, France\nThe topological derivative quantifi
 es the sensitivity of objective functionals whose evaluation involves the 
 solution of a PDE with respect to the nucleation of a small feature (e.g. 
 cavity\, inclusion\, crack) at a prescribed location in the (e.g. acoustic
 \, elastic\, electromagnetic) medium of interest. Originally formulated in
  the context of topology optimization\, the concept of topological derivat
 ive has also proved effective as a qualitative inversion tool for wave-bas
 ed identification of either small or finite-sized objects. In that approac
 h\, hidden objects are deemed to lie at locations where the topological de
 rivative is most negative. Topological derivatives need asymptotic analysi
 sfor their derivation\, but are then very simple to implement and entail c
 omputational costs that are much lower than straightforward optimization-b
 ased inversion methods. Focusing on acoustic and elastodynamic scattering\
 , and stressing main concepts and results rather than technical detail\, t
 he following topics will be addressed: 1) An overview of inverse scatterin
 g approaches relying on asymptotic expansions for small scatterers. 2) Asu
 mmarized presentation of the derivation of topological derivatives for aco
 ustic and elastodynamic scattering\, including small-inclusion asymptotics
  based on the expansion of Lippmann-Schwinger volume integral equations. 3
 ) The implementation of topological derivative and numerical experiments. 
 4) Going beyond the above heuristic-based use of the topological derivativ
 e\, a (partial in scope) justification is presented for the acoustic\ncase
  involving far-field measurements (collaboration with Cedric Bellis and Fi
 oralba Cakoni). 5) Higher-order expansions\, providing approximations of o
 bjective functionals that are polynomial in the defect diameter (with coef
 ficients depending on trial defect location and assumed physical propertie
 s) and permitting quantitative identification within moderate computationa
 l costs\, will finally be addressed\nBio :  Marc Bonnet\, a CNRS senior s
 cientist\, is with the POEMS group of the Applied Mathematics department o
 f ENSTA since 2011\, and was before that with the Solid Mechanics laborato
 ry (LMS) of Ecole Polytechnique. He completed master studies in solid mech
 anics in 1983 (université Paris 6\, concurrently with the engineering deg
 ree of ENPC\, Paris)\, obtained his doctor degree from ENPC in 1986 and hi
 s habilitation degree from Université Paris 6 in 1995. His research inter
 ests include inverse problems\, integral equation methods and asymptotic m
 odels for elastic and acoustic wave propagation problems. He is associate 
 editor or editorial board member of several international research journal
 s (Inverse Problems\, Engineering Analysis for Boundary Elements\, Journal
 \nof Integral Equations and Applications\, Inverse Problems in Engineering
  and Sciences\, Computational Mechanics\, Journal of Optimization Theory a
 nd Applications).
LOCATION:GCB330 http://plan.epfl.ch/?lang=fr&room=GCB330
STATUS:CONFIRMED
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