Numerical analysis and partial differential equations.

Course coordinator : K. Schratz

The Major degree Numerical Analysis & Partial Differential Equations (ANEDP) is one of the Majors proposed by the Mathematics of Modelling speciality, second year of the Masters in Mathematics and Applications.

The main degree ANEDP aims at educating:

The ANEDP Major's key topic is the theoretical and numerical study of modeled problems by linear and nonlinear partial differential equations from various fields such as physics, engineering, chemistry, biology,  economy, as well as methods of scientific computing aiming at the digital simulation of these problems. Scientific computing has become the key element of technological progress. It requires a deep understanding of mathematical modelling, numerical analysis, and computer science. The broad portfolio of courses of the Major allows students to explore and manage the various aspects of these disciplines. The various fields of mathematics concerned are diversified and developing quickly; their development involves an increasing need for mathematicians. One of the goals of this major is to train such mathematicians. The courses offered cover the following fields:

  1. The mathematical modelling of many application areas: solid mechanics, fluid mechanics, propagation phenomena (acoustic, seismic, electromagnetism), the treatment of signal and image, finance, chemistry and combustion.
  2. Mathematical analysis of linear and nonlinear partial differential equations (existence, unicity and regularity of solutions).
  3. Methods of appoximation: finite elements, finite differences, spectral methods, particulate methods, wavelets.
  4. computer implementation of these methods and design of scientific computing software.
Course title Lecturer(s) Type Course Code
PDE and randomness : a few examples Antoine Gloria Fundamental MU5MAM40
Introduction to evolution PDE Katharina Schratz Fundamental MU5MAM12
Cinetic models and hydrodynamic limits François Golse Fundamental MU5MAM28
High performance computing for numerical methods and data analysis Laura Grigori, Emile Parolin Fundamental MU5MAM29
From EDP to their resolution by finite elements Didier Smets, Pierre-Henri Tournier Fundamental MU5MAM30
EDP et modélisation Frédéric Legoll Fundamental MU5MAM92
Probabilistic Numerical Methods Julien Reygner Fundamental MU5MAM35
Réduction de dimension linéaire et nonlinéaire Applications aux EDP, problèmes inverses et science des données Albert Cohen Fundamental
Quelques grands algorithmes d’hier et d’aujourd’hui Bruno Després (coordinator) Fundamental
Variational approximations of PDEs Yvon Maday Fundamental MU5MAM36
Elliptic equations Hoai-Minh Nguyen Fundamental MU5MAM47
Analyse théorique et numérique des équations hyperboliques Amaury Hayat, Alexandre Ern Fundamental MU5MAM41
Optimisation sous contraintes d’EDP Beniamin Bogosel Fundamental
Analyse des effets géométriques sur les équations dispersives Oana Ivanovici Specialised
Flots de gradient et particules en interaction en théorie de l’apprentissage Borjan Geshkovski Specialised
Systèmes paraboliques Ayman Moussa Specialised
Limites de champ moyen Sylvia Serfaty Specialised
Méthodes de tenseurs pour la résolution d'EDPs en grande dimension Virginie Ehrlacher, Mi-Song Dupuy Specialised MU5MAM84
Autour de la stabilité de l'espace-temps de Minkowski Jérémy Szeftel Specialised MU5MAM42
Modèles hyperboliques d'écoulements complexes dans le domaine de l’océanographie, des risques naturels et de l'énergie Jacques Sainte-Marie, Nina Aguillon Specialised MU5MAM27
Spectral theory and variational methods Eric Cancès & Mathieu Lewin Specialised MU5MAM87
Modern methods and algorithms for parallel computation Frédéric Nataf Specialised MU5MAM50
Discontinuous Galerkin methods and applications Alexandre Ern Specialised MU5MAM21
Mathematical methods and numerical analysis for molecular simulation. Gabriel Stoltz Specialised MU5MAM38
Du fluide de Stokes aux suspensions de solides rigides : aspects théoriques et numériques Aline Lefebvre-Lepot, Flore Nabet Specialised MU5MAM43
Modèles mathématiques et méthodes numériques pour la simulation en hémodynamique Miguel Fernández Specialised MU5MAM90
Réseaux de neurones et approximation numérique adaptative Bruno Després Specialised MU5MAM91
Jeux à champ moyen Charles Bertucci Specialised MU5MAM88