The Factas team is the sequel of the Apics team that ended in 2017.
Functional Analysis for ConcepTion and Assessment of Systems
The mathematical body of knowledge shared by the team members involves functional and harmonic analysis along with related fields like approximation theory, potential theory, asymptotic analysis, or system theory.
Our approach is to couple these tools with constructive optimisation techniques, and to demonstrate the efficiency of such a combination in selected application areas, mostly for inverse problems in electromagnetics. These applications concern paleomagnetism in planetary sciences and imaging issues in electro- and magneto-encephalography (EEG and MEG) for functional and medical neurosciences, in quasi-static situations, together with scattering issues related to wave equation for shape identification in frequency domain.
The behaviour of underlying quantities (electric potential, electromagnetic fields) is modelled by Maxwell equations, thereby by Poisson or Helmholtz partial differential equations (PDE) in the above frameworks.
The team considers inverse problems that consist in source estimation, data transmission, parameter or geometrical/shape identification issues, from available measurements. Their regularisation and resolution is performed through appropriate approximation which is consistent with the problem structure and whose error can be quantified.
We try to balance theoretical and applied work without sacrificing any, a transverse positioning made possible by the complementary skills within the team, ranging from mathematical analysis to algorithm design, numerical optimisation, prototypical software design.