Time Reversed Absorbing Conditions (TRAC) in the Time and Frequency Domains

Franck  Assous; Frédéric  Nataf; Marie  Kray; Eli  Turkel

1st International ICST Workshop on New Computational Methods for Inverse Problems

Research Article

Time Reversed Absorbing Conditions (TRAC) in the Time and Frequency Domains

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.4108/icst.valuetools.2011.245812,
    author={Franck  Assous  and Fr\^{e}d\^{e}ric  Nataf  and Marie  Kray and Eli  Turkel },
    title={Time Reversed Absorbing Conditions (TRAC) in the Time and Frequency Domains},
    proceedings={1st International ICST Workshop on New Computational Methods for Inverse Problems},
    publisher={ACM},
    proceedings_a={NCMIP},
    year={2012},
    month={6},
    keywords={Time Reversed Absorbing Conditions Frequency Domains},
    doi={10.4108/icst.valuetools.2011.245812}
}

Franck Assous
Frédéric Nataf
Marie Kray
Eli Turkel
Year: 2012
Time Reversed Absorbing Conditions (TRAC) in the Time and Frequency Domains
NCMIP
ICST
DOI: 10.4108/icst.valuetools.2011.245812

Franck Assous ¹^,*, Frédéric Nataf ², Marie Kray³, Eli Turkel ⁴

1: Department of Mathematics Bar-Ilan University & Ariel Center University Israel
2: Department of Mathematics Bar-Ilan UPMC Université Paris 6 Laboratoire J.L. Lions 75005 Paris, France
3: UPMC Université Paris 6 Laboratoire J.L. Lions 75005 Paris, France
4: UPMC Université Paris 6 School of Mathematical Sciences Tel-Aviv University 69978 Ramat Aviv, Israel

*Contact email: franckassous@netscape.net

Abstract

We 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 that 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 es- timate for the resulting non-standard boundary value prob- lem. Numerical tests are presented in two dimensions for the wave and the Helmholtz equation. In particular the TRAC method is applied to the differentiation between a single in- clusion and a two close inclusion case. This technique is fairly insensitive with respect to noise in the data.

Keywords: Time Reversed Absorbing Conditions Frequency Domains

Published: 2012-06-26
Publisher: ACM

: http://dx.doi.org/10.4108/icst.valuetools.2011.245812