Partial differential equations play a fundamental role in modeling complex phenomenon in fields as varied as mechanics, physics, and biology. Since the 1950s and the advent of computers, the development and use of numerical methods for the approximate machine calculation of solutions to partial differential equations have become routine in engineering. In automotive engineering, for example, not only deformations of the passenger compartment in the event of an impact but also air conditioning, ambient noise and electromagnetic compatibility are nowadays calculated by computer.
The course aims to highlight the link between classical mechanical and physical models based on partial differential equations, the underlying mathematical analysis, and the development of the finite element method. The common thread will be the variational point of view, which enables problems to be rewritten as minimization problems, making the link with optimization. A significant part of the course will be devoted to machine implementation of the finite element method and to the explicit approximate solution of certain partial differential equations using FreeFem++ software. In particular, students will be asked to carry out a mini-project using this software.
In addition, some of the PCs will illustrate on computer the concepts seen in class.
Evaluation: A written exam, quiz and mandatory mini-project.
- Teaching coordinator: Chesnel Lucas
- Teaching coordinator: Moireau Philippe
- Teaching coordinator: Nabet Flore