Analysis, Numerical Analysis, and Scientific Computing
Director : Nicolas SEGUIN
Research Topics :
The ACSIOM team is well-known for its scientific research on partial derived equations, as well as theoretical and digital maps. These equations are studied particularly for their applications in mechanics, biology, and ecology. ACSIOM also houses two subtopics: “Digital Analysis and Scientific Calculaton” and “Analysis of EDP, Convex Analysis, and Optimization”. The team has numerous national, international, and local projects, including collaborations with important players in the industrial world: EPF, HORIBA, Safran, Saint-Gobain, Total, etc. ACSIOM also actively participates in local development initiatives, such as I-SITE MUSE and the LabEX NUMEV.
Digital Analysis and Scientific Calculation :
The topic of Digital Analysis and Scientific Calculation encompasses the development and analysis of of advanced numerical methods and their applications to physical systems. Along with methodological developments, it also includes the design and analysis of discretization methods for high-order EDP’s on polyhedral meshes, form optimization methods, etc. These methods have the goal of resolving mechanical problems: fluid-structure interactions, large-scale simulations of turbulence, and poromechanical flow, etc. There are many applications, including: blood discharges, coastal discharges, nuclear power production, and waste storage, etc.
Analysis of EDP, Convex Analysis, and Optimization :
The topic of EDP analysis is developed around applications linked particularly to the mechanics and dynamics of populations. Beyond the usual questions of the existence, uniqueness and regularity of solutions to equations, we are also interested in the qualitative properties of solutions obtained from different types of asymptotic analysis: homogenization, multiple scales, boundary layer, long-time behavior… The Control activity is developed in harmony with the topic of optimization around the analysis and the control of dynamic systems (dissipative and gradient), the study of attainable sets of differential inclusions, and form optimization problems. The IMAG mathematics laboratory runs the international journal: Journal of Convex Analysis.