Acquire the theoretical and practical backgrounds for the numerical approximation of (systems of) PDEs of elliptic, parabolic or hyperbolic types using Finite Element and Finite Volumes Methods.
- Enseignant: Simon LEMAIRE
- Enseignant: Thomas Rey
A course in three parts, introducing the student to mathematical modeling in different physical contexts.
- Enseignant: Stephan De Bievre
- Enseignant: André De Laire
- Enseignant: Maxime Herda
Acquire the theoretical and practical backgrounds for the numerical approximation of ODEs and PDEs using standard numerical methods:
1) One-step methods for ODEs: introduction to ODES, Cauchy-Lipschitz theorem, development of numerical methods, convergence analysis
2) Finite difference method for usual linear PDEs: introduction to PDEs, principle of the finite difference method, application to Poisson and heat equations in 1D.
3) Finite element method for elliptic linear PDEs: variational formulation and Lax-Milgram theorem, variational approximation and convergence study, algorithmic implementation in 1D of Lagrange P1 finite elements.
4) Resolution of linear systems: basics of linear algebra, direct methods, iterative methods.
- Enseignant: Claire Chainais-Hillairet
- Enseignant: André De Laire
The objective of this teaching is to enable the student to understand the numerical methods used to solve models describing low frequency electromagnetic phenomena. This knowledge is now essential to understand, design and improve complex electromagnetic systems.
- Enseignant: Thomas Henneron
- Enseignant: Yvonnick Le Menach
- Enseignant: Zuqi Tang