Numerical analysis and partial differential equations.

Course coordinator : D. Smets

The Major degree Numerical Analysis & Partial Differential Equations (ANEDP) is one of five Majors proposed by the speciality Mathematics of Modelling, 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
Probabilistic Numerical Methods Tony Lelièvre Fundamental MU5MAM35
Elliptic equations Antoine Gloria Fundamental MU5MAM47
Introduction to evolution PDE Katharina Schratz Fundamental MU5MAM12
From EDP to their resolution by finite elements Xavier Claeys Fundamental MU5MAM30
Variational approximations of PDEs Yvon Maday Fundamental MU5MAM36
Reject [CG] Theoretical and Numerical Aspects Frédéric Legoll Fundamental MU5MAM34
Theoretical and Numerical Analysis of Hyperbolic Systems of Conservation Laws Grégoire Allaire Fundamental MU5MAM16
High performance computing for numerical methods and data analysis Laura Grigori Fundamental MU5MAM29
Introduction to stochastic PDEs Anne de Bouard Fundamental MU5MAM63
Approximation et traitement de données en grande dimension Albert Cohen Specialised MU5MAM73
Lorentzian geometry and hyperbolic PDE Jacques Smulevici Specialised MU5MAM75
Theoretical and numerical aspects of incompressible fluids Pascal Frey, Yannick Privat Specialised MU5MAM57
Reaction-diffusion equations and dynamics of biological populations Henri Berestycki Specialised MU5MAM05
Hyperbolic models for complex flow in the field of energy Jacques Sainte-Marie 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
Cinetic models and hydrodynamic limits François Golse Specialised MU5MAM28
High performance computing, parallel computation algorithms in large-scale linear algebra, numerical stability Laura Grigori Specialised MU5MAM29
Optimisation de formes: aspects géométriques et topologiques Samuel Amstutz Specialised MU5MAM78
Fluid dynamics models in life sciences, mathematical and computational viewpoints Laurent Boudin & Miguel Fernandez Specialised 5MM26
Optimal transport : theory and applications Max Fathi Specialised 5MM07
Analyse d’edp non-linéaires issues de la géométrie : des applications harmoniques à la théorie de Yang-Mills Paul Laurain Specialised MU5MAM72
Réseaux de neurones et approximation numérique adaptative Bruno Després Specialised MU5MAM86