Modelling reality through mathematical models and building algorithms optimised for numerical simulations poses scientific and technological challenges that are at the heart of several academic and industrial fields. The heart of this project is the mathematical modelling of problems arising from various applications for the environment and living. The proposed modelling will be considered through the use of partial differential equations: this is a strong field of investigation within Normandy.The project will be organised around four axes (with strong links and collaborations between these axes):1) Innovations for energy (digital modelling and simulations for wind and hydropower, energy efficiency of buildings and data center)2) Smart City (Modelisation and optimisation of traffic on a metropolitan scale, driving aid and autonomous vehicles)3) Mathematical modelling for innovative materials (active materials, composite materials)4) Imagery modelling and simulation (segmentation and recaling, inverse imaging problems, medical imaging applications, additive manufacturing)In this project, we focus on various theoretical aspects (existence and uniqueness of a solution, convergence problems, control, homogenisation) and numerical analysis and simulation (finite differences, finite volumes, finite elements) in order to write algorithms that will then be implemented in connection with the CRIANN Computation Center in particular, because the computational needs are important, considering the large volumes of data that we will have to process in our applications. This is therefore a project structuring at the heart of Axis 5 (Analytic Structures and Models, scientific calculus) of the strategic research and training centre “Sciences du Numérique” at Normandie University and is quite naturally integrated into the RIN Normandie Digitale. It brings together more than thirty Norman researchers from all the laboratories of mathematics (LMAH, LMI, LMNO, LMRs) and computer science (LITIS, GREYC, IRSEEM) in Normandy as well as laboratories engaged in partnership research, particularly around high performance simulation (CORIA and LMN).
