1. Modeling, numerical simulation, mathematical models

In the 1960s-1970s, the aerospace, automotive and energy industries, particularly the nuclear sector, began using numerical simulation to study the behavior and validate the design of components and structures, thanks to the development of limited software for internal use. This software has become increasingly robust in terms of algorithms, calculation performance, automatic mesh preparation and results analysis tools. The mathematical model is a partial differential equation that describes the physical phenomenon. For example, Laplace's equation can be used to calculate the propagation of heat by conduction in solids. The finite element modeling and numerical simulation approach is based on the discretization of the mathematical model adapted to the physical phenomenon under study.

On the scientific front, France occupies a privileged position internationally...