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Programme ANEDP

Under the LMD (Bachelors, Masters, Doctorate) system, ANEDP (numerical analysis and partial differential equations) consists of a theoretical component  – coursework and exams (30 ECTS) – and a practical component, which is an initiation to research combined with the presentation of a dissertation to a panel (24 ects).

A further 6 ECTS are needed to reach the total of 60 ects required to complete the second year of the Masters (M2).These can be obtained either by attending the UPMC’s “Modelling Option Seminar” (code NM452), or by passing an additional examination, agreed in consultation with the course director.In the latter case, it is essential to state your choice before the normal examination session on the ANEDP programme.

The final grade, which determines your ranking in the M2 ANEDP degree, is the weighted average of the score awarded for theory and the score in the research dissertation.

Course programme

First semester: foundation course + specialist course

Second semester:specialist course

The courses in the ANEDP programme are divided into work on the foundation and specialist subjects.

The basics classes in the first semester provide a grounding in all the essential concepts that form the core knowledge base in the Modelling Mathematics speciality:

  • Theoretical and numerical analysis of conservation law hyperbolic systems by Prof Frédéric COQUEL
  • A course on homogenization by Prof Grégoire ALLAIRE
  • Elliptical equations by Prof Fabrice BETHUEL
  • Variational approximations of partial differential equations by Prof Albert COHEN
  • Introduction to finite volumes methods by Prof Bruno DESPRES
  • Theory of evolution equations by Prof Isabelle GALLAGHER  
  • From PDEs to their numerical solution by finite element methods (a theoretical introduction with 
  •   a C++ implementation) by Frédéric HECHT
  • Probabilistic numerical methods by Prof Tony LELIEVRE
  • Advanced numerical matrix analysis and parallel calculus by François-Xavier ROUX

The specialist courses introduce up-to-the-minute topics and develop further techniques currently used by researchers.

The first semester courses are:

  • Control and nonlinearity by Prof Jean-Michel CORON
  • Nonlinear dispersive PDEs and applications in optics by Prof Anne DE BOUARD
  • Fluid-structure interaction.Application to blood flows by Profs Céline GRANDMONT and Yvon MADAY
  • Growth, reaction, movement and dispersion from biology by Benoît PERTHAME
  • Partial differential equations:control and numerical aspects by Prof Enrique ZUAZU

The second semester courses are:

  • Partial differential equations:control and numerical aspects by T ABBOUD
  • Reaction equations – dispersion and dynamics of biological populations by Profs Henri Berestycki and Grégoire Nadin
  • Modelling and simulation of atoms and molecules in quantum physics by Profs Eric CANCES and Mathieu LEWIN
  • Mathematical models for inverse problems by Profs Antonin CHAMBOLLE and Houssem HADDAR
  • Convex optimisation and applications to signal processing by Prof Patrick-Louis COMBETTES
  • Discontinuous galerkin methods and applications by Profs Alexandre ERN and Daniele Antonio DI PIETRO
  • Advanced numerical simulation methods by Prof Pascal FREY
  • Hyperbolic models for complex flows in energy by Profs Edwige GODLEWSKI and Nicolas SEGUIN
  • Kinetic models by Prof François GOLSE
  • Multiscale problems.Theoretical and numerical aspects by Prof Frédéric LEGOLL
  • Mathematical study of waves and other free-surface problems by Prof David LANNES      
  • Viscosity solutions for nonlinear PDEs and finite difference schemes by Prof Régis MONNEAU
  • Modern parallel calculus methods and algorithms by Prof Frédéric NATAF
  • The effect of dispersion in nonlinear parabolic systems by Prof Philippe SOUPLET
  • Numerical approximation of Vlasov - Maxwell equations by Prof Eric SONNENDRÜCKER
  • Retrospective estimates for effective calculations and error checking by Prof Martin VOHRALIK

The refresher courses are designed to reiterate the theoretical and practical elements needed to follow the classes.They are tested.All students are advised to attend the refresher courses so that they can compare their level of knowledge with what they will subsequently need…

The “majors”

The ANEDP programme introduces the concept of “major” in order to raise student awareness about topics of significant future relevance.For the moment, three majors have been established:

  • Energy for the future
  • Advanced modelling, simulation and visualisation methods
  • Scientific calculus