Time reversed absorbing conditions

Franck Assous; Marie Kray; Frédéric Nataf; Eli Turkel

doi:10.1016/j.crma.2010.09.014

Partial Differential Equations/Numerical Analysis

Time reversed absorbing conditions
[Conditions aux limites absorbantes retournées temporellement]

Présenté par : Olivier Pironneau

Franck Assous ^1,² ; Marie Kray ³ ; Frédéric Nataf ³ ; Eli Turkel ⁴

¹ Bar Ilan University, 52900 Ramat Gan, Israel
² Ariel University Center, 40700 Ariel, Israel
³ UPMC Université Paris-06, UMR 7598, laboratoire J.L. Lions, 75005 Paris, France
⁴ Tel-Aviv University, 69978 Ramat Aviv, Israel

Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1063-1067.

Résumé
Abstract

Le but de cette note est d'introduire les conditions absorbantes retournées temporellement (TRAC) dans les méthodes de retournement temporel. Elles rendent possible la « reconstruction du passé » sans connaître la source émettrice des signaux enregistrés puis rétropropagés. Cette nouvelle méthode ne nécessite pas de connaissance a priori des propriétés physiques de l'inclusion. Nous démontrons une estimation d'énergie pour le problème non standard obtenu. Deux applications aux problèmes inverses sont proposées.

The aim of this note is to introduce the time reversed absorbing conditions (TRAC) in time reversal methods. These new boundary conditions enable one to “recreate the past” without knowing the source which has emitted the signals that are back-propagated. This new method does not rely on any a priori knowledge of the physical properties of the inclusion. We prove an energy estimate for the resulting non-standard boundary value problem. Two applications to inverse problems are given.

Reçu le : 2010-08-09
Accepté le : 2010-09-08
Publié le : 2010-10-01

DOI : 10.1016/j.crma.2010.09.014

Affiliations des auteurs :

Franck Assous ^{1, 2} ; Marie Kray ³ ; Frédéric Nataf ³ ; Eli Turkel ⁴

¹ Bar Ilan University, 52900 Ramat Gan, Israel
² Ariel University Center, 40700 Ariel, Israel
³ UPMC Université Paris-06, UMR 7598, laboratoire J.L. Lions, 75005 Paris, France
⁴ Tel-Aviv University, 69978 Ramat Aviv, Israel

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Franck Assous; Marie Kray; Frédéric Nataf; Eli Turkel. Time reversed absorbing conditions. Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1063-1067. doi : 10.1016/j.crma.2010.09.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.014/

Bibliographie
Cité par

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Marie Graff; Mina Cullen TRAC method in dissipative media – a first analysis in frequency domain and homogeneous media, Inverse Problems, Volume 39 (2023) no. 6, p. 31 (Id/No 064007) | DOI:10.1088/1361-6420/acd272 | Zbl:7691087
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Tomer Levin; Eli Turkel; Dan Givoli Obstacle identification using the TRAC algorithm with a second-order ABC, International Journal for Numerical Methods in Engineering, Volume 118 (2019) no. 2, pp. 61-92 | DOI:10.1002/nme.6003 | Zbl:1548.65192
Marie Graff; Marcus J. Grote; Frédéric Nataf; Franck Assous How to solve inverse scattering problems without knowing the source term: a three-step strategy, Inverse Problems, Volume 35 (2019) no. 10, p. 20 (Id/No 104001) | DOI:10.1088/1361-6420/ab2d5f | Zbl:1426.78020
Adar Kahana; Eli Turkel; Dan Givoli Convective Wave Equation and Time Reversal Process for Source Refocusing, Journal of Theoretical and Computational Acoustics, Volume 26 (2018) no. 02, p. 1850016 | DOI:10.1142/s2591728518500160
Maya de Buhan; Marie Kray A new approach to solve the inverse scattering problem for waves: combining the TRAC and the adaptive inversion methods, Inverse Problems, Volume 29 (2013) no. 8, p. 085009 | DOI:10.1088/0266-5611/29/8/085009
F. Assous; M. Kray; F. Nataf Time-reversed absorbing conditions in the partial aperture case, Wave Motion, Volume 49 (2012) no. 7, pp. 617-631 | DOI:10.1016/j.wavemoti.2012.03.006 | Zbl:1360.35314
Caroline Baldassari; Hélène Barucq; Henri Calandra; Julien Diaz Numerical performances of a hybrid local‐time stepping strategy applied to the reverse time migration, Geophysical Prospecting, Volume 59 (2011) no. 5, p. 907 | DOI:10.1111/j.1365-2478.2011.00975.x
F Assous; M Kray; F Nataf; E Turkel Time-reversed absorbing condition: application to inverse problems, Inverse Problems, Volume 27 (2011) no. 6, p. 065003 | DOI:10.1088/0266-5611/27/6/065003

Cité par 10 documents. Sources : Crossref, zbMATH

^☆ This work was supported by the French–Israeli Grant FIST-MATHS2.

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