IDEFIX

The research activity of our team is dedicated to the design, analysis and implementation of efficient numerical methods to solve application oriented inverse problems in connection with Partial Differential Equations (PDEs). Sought practical applications include non destructive testing, X-ray, electromagnetic (radar) and ultrasound imaging, bio-medical modeling and imaging, acoustics and sound modeling, spatial audio simulation, invisibility and meta-materials design.
Roughly speaking, a generic problem would consist in determining the geometry (with unknown topology!) and/or physical properties of unknown targets from indirect measurements. In general this kind of problems are non-linear and are also severely ill-posed which require special attention from regularization point of viewand non-trivial adaptations of classical optimization methods.
We are particularly interested in the development of fast methods that are suited for real-time applications and/or large scale problems. These goals require to work on both the physical and the mathematical models involved and indeed a solid expertise in related numerical algorithms.
Our scientific research interests are the following:

• Theoretical understanding and analysis of the forward and inverse mathematical models (PDE), including in particular the development of reduced models.
• Design and study of algorithms capable of treating non linear problems, robust with respect to noise and/or suited for real time imaging and audio.
• Development of new methods and advanced tools for HPC to solve large scale forward and/or inverse problems.
• Development of prototype softwares for practical applications and general toolboxes and advising of industrial software development.