DEFI Research team
Shape reconstruction and identification
Team presentationThe research activity of our team is dedicated to the design, analysis and implementation of efficient numerical methods to solve inverse and/or shape and topological optimization problems in connection with acoustics, electromagnetism, elastodynamics, and waves in general.
Sought practical applications include radar and sonar applications, bio-medical imaging techniques, non-destructive testing, structural design, composite materials, ...
Roughly speaking, the model problem consists in determining information on, or optimizing the geometry (topology) and/or the physical properties of unknown targets from given constraints or measurements, for instance measurements of diffracted waves. In general this kind of problems is non linear. The inverse ones are also severely ill-posed and therefore require special attention from regularization point of view, and non trivial adaptations of classical optimization methods.
Our scientific research interests are three-fold:
- Theoretical understanding and analysis of the forward and inverse mathematical models, including in particular the development of simplified models for adequate asymptotic configurations.
- The design of efficient numerical optimization/inversion methods which are quick and robust with respect to noise. Special attention will be paid to algorithms capable of treating large scale problems (e.g. 3-D problems) and/or suited for real-time imaging.
- Development of prototype softwares for precise applications or tutorial toolboxes.
- Non-iterative methods for inverse boundary value problems, inverse scattering problems and imaging (Samplings methods for multistatic data at a fixed frequency, Asymptotic methods, Qualitative estimates for target identification problems, ...)
- Shape and topological optimization methods with application to inverse problems (Homogenization and small amplitude homogenization methods, Level Set methods, Toplogical gradient methods, ...)
- Hybrid methods
- Regularization and stability issues for ill-posed problems and imaging (Stability estimates, Methods of total variation, Edge preserving image reconstructions, ...)
International and industrial relations
- DGA, CEA, Onera, Total, Cerfacs
- Universities of Delaware (USA), Goettingen (Germany), ENIT (Tunisia), ITU (Turkey), Genova (Italy).
Research teams of the same theme :
- BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
- CAD - Computer Aided Design
- CAGIRE - Computational Approximation with discontinous Galerkin methods and compaRison with Experiments
- CALVI - Scientific computation and visualization
- CASTOR - Control, Analysis and Simulations for TOkamak Research
- COFFEE - COmplex Flows For Energy and Environment
- CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods
- GAMMA3 - Automatic mesh generation and advanced methods
- IPSO - Invariant Preserving SOlvers
- MC2 - Modeling, control and computations
- MICMAC - Methods and engineering of multiscale computing from atom to continuum
- MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
- NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
- NANO-D - Algorithms for Modeling and Simulation of Nanosystems
- OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
- POEMS - Wave propagation: mathematical analysis and simulation
- SCIPORT - Program transformations for scientific computing
- SIMPAF - SImulations and Modeling for PArticles and Fluids