Objective Inverse problems that are governed by partial differential equations arise in many applications in computational science and engineering. Solving these large scale problems is a real challenge to the existing numerical methods, as they are generally highly ill-posed and non-convex. These difficulties are usually handled by introducing statistical Bayesian estimation methods that promote a-priori knowledge to the problems. Such methods address the uncertainties in the inverse problems, such as the noise and unknown parameters, so that the solution of the inverse problems is meaningful and realistic. Additionally, numerically solving these large-scale problems requires highly efficient and scalable numerical methods, which are still missing or inadequate for many applications.Multiscale and multigrid methods are extremely efficient and scalable for some applications, but there are other problems that still pose severe challenges. In this research I plan to study two problems: one is the challenging inverse wave equation, which appears in many applications such as seismic exploration of reservoirs, and medical imaging. The other problem is the rather unexplored 4D imaging of flow in porous media, used for monitoring of reservoirs, carbon sequestration among other applications. I plan to develop efficient multiscale (and multigrid) methods for some of the key ingredients of the numerical solution of these problems. Such methods may enable a scalable and efficient solution of these inverse problems. In particular, to solve the inverse wave equation, one needs to efficiently solve the Helmholtz equation, which is still considered an open question. Another example is a multiscale approach for efficiently estimating an inverse of a covariance matrix given a few measurements. This problem lies in the heart of statistical Bayesian estimation methods, and it can be addressed if one considers the structure of the covariance for the problems of interest. Fields of science natural sciencescomputer and information sciencescomputational sciencenatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsengineering and technologymedical engineeringdiagnostic imagingnatural sciencesmathematicsapplied mathematicsnumerical analysis Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) FP7-PEOPLE-2013-IOF - Marie Curie Action: "International Outgoing Fellowships for Career Development" Call for proposal FP7-PEOPLE-2013-IOF See other projects for this call Funding Scheme MC-IOF - International Outgoing Fellowships (IOF) Coordinator BEN-GURION UNIVERSITY OF THE NEGEV EU contribution € 264 079,80 Address . 84105 Beer Sheva Israel See on map Activity type Higher or Secondary Education Establishments Administrative Contact Lori Liss (Mrs.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Participants (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY Participation ended Israel EU contribution No data Address SENATE BUILDING TECHNION CITY 32000 Haifa See on map Activity type Higher or Secondary Education Establishments Administrative Contact Mark Davison (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
