**Frédéric Hecht**, Pierre et Marie Curie University, Laboratory Jacques-Louis Lions

"I would like it to be possible to solve digitally, in a user-friendly way, the problems modeled by partial differential equations (PDEs) from physics, engineering, computing graphics and recently from the finance-banking sector. This problem is therefore at the interface between applied mathematics, numerical analysis, computer science and the relevant applications (fluid mechanics, electromagnetism, quantum mechanics and stock options in finance)." |

**Tuesday, August 22, **10:00AM-12:00PM

Mike Sussman: expository lecture on FreeFem++

**Wednesday, August 23, **1:00PM-3:00PM

Mike Sussman: expository lecture on FreeFem++

**Friday, August 25, **1:00PM-3:00PM

Alicia Klinvex: expository lecture on FreeFem++

**Monday, August 28**

** Frédéric Hecht: **FreeFem++ basics

*Morning: *10:00AM-12:00PM

- Introduction to FreeFem++ 2d : installation, mesh, finite element, weak formulation, linear solver, graphics
- The Poisson/ Laplace Problem : weak formulation, boundary condition problem, first example
- Problem in Time on Heat equation
- Non Linear equation
- Newton Method

*Afternoon*: 2:00PM-3:00PM

Working class on Laptop : How to install, Examples on verification of estimate on Poisson problem, Examples on Heat problem on an Oven**Tuesday, August 29**

**Frédéric Hecht: Some Freefem++ tools**

*Morning: *10:00AM-12PM

Matrix/vector usage, Mesh Adaptation, Eigen value problem, Optimisation tools : ipopt, Stokes and Incompressible Navier-Stokes Problem (Some formulatio, Boundary Condition for the Stokes problem, Some numerical scheme for the Navier-Stokes: Newton Method, Characteristic method, Chorin Algorithm, Boussinesq equation)

*Afternoon*: 2:00PM-3:00PM

An Optimization Problem - Minimal surface problem, and The Optimisation of the Oven problem with and without fluid. **Wednesday, August 30**

** ****Frédéric Hecht: FreeFem++ 3D computation and coupling problem**

*Morning: *10:AM-12:00PM

- 3d Mesh tools, tetgen, buillayer
- 3d problem: Navier-Stokes, Elasticity problem, Boussinesq
- Other mathematical formulation: Mixed Finite Element, DG formulation

*Afternoon*: 2:00PM-3:00PM

Try to make the 2D/3D fluid benchmark.

**Thursday, August 31**

**Frédéric Hecht: FreeFem++ **parallel computing

*Morning*: 10AM-12PM

Presentation of the mpi tool of freefem++, parallel solver, DDM method in freefem++*Afternoon*: 2:00PM-3PM

Test of the mpi version if possible, Simple parallisation trick, paralelisation of the Chorin Algorithm for Navier-Stokes in 3d.

**Friday, September 1: Department of Mathematics colloquium**