Research interests
I obtained my Ph.D. in Applied Mathematics from the University of Paris IX, France in
December 1999 with highest level of distinction. The domain of my expertise is Numerical Analysis and in
particular I have been working on the development, analysis and implementation of efficient numerical
methods for wave propagation problems. My main contributions are
in the following areas: fictitious domain methods, higher-order finite
elements with mass-lumping and techniques for treating
unbounded media (absorbing boundary conditions and perfectly matched
layers). On this subject, I have 14 publications in peer-reviewed
international journals which total 539 citations (excluding
self-citations; source: ISI Web of Knowledge and Google Scholar), 3
chapters in collective volumes and more than 20 presentations in
international conferences.
In parallel to my research on forward wave propagation problems, I
have also been working on inverse problems and more precisely on time reversal and imaging. Imaging with waves
in complex media is the main area of my current activities. My research in this area
was initiated during my post-doctoral position at Stanford University
(2000-2001). My main collaborators are L. Borcea (University of Michigan) and
G. Papanicolaou (Stanford University). Together we have
developed statistically stable
methodologies for imaging in cluttered media. The word clutter here
describes inhomogeneities in the wave speed of the propagation medium
that are unknown and we model with random processes. More precisely,
we are interested in imaging in a regime where multipathing due to the
inhomogeneities is significant. Imaging in
such regimes is quite challenging and requires very different methods
from the usual ones. Since 2010 a close collaboration with J. Garnier
(University Paris Diderot) has been also established. My most recent activities concern the development and
analysis of correlation based imaging and velocity estimation techniques that rely on ambient noise recordings
associated to natural or anthropogenic activities in our environment. The key idea exploited is that
information about the Green’s function in the medium can be obtained from cross-correlations of noisy signals.
To resume, my work on imaging is very well known in the Inverse
Problems community. In this area, I have 27 publications in peer-reviewed international
journals which total 533 citations (excluding self-citations; sources: ISI Web of Knowledge
and Google Scolar), 1 chapter in collective volumes and more than 25 invited presentations
in international conferences.
Research grants
- European Research Council Stanting Grant, GA 239959
(PI)
- European grand under the FP7 regional potential program,
GA 245749 (CO-PI)
- Marie Curie International Reintegration
Grant MIRG-CT-2007-203438. (PI)