Modelling

Objectifs

At the end of this module, the student should have understood and be able to explain the following notions for each subject :

¿ Mechanics : understanding the behaviour of a moving solid subjected to external actions.

¿ Introduction to numerical modelling : fundamentals of the finite difference method (order of a scheme, stability, discrete maximum principle, convergence); formal definition of the Brownian motion and principles of the Monte-Carlo method for parabolic PDEs; the use of PDE for modelling problems with continuous variables.

¿ Modelling project : how to model mathematically and numerically a given industrial ¿ engineering - scientific problem.

The student should have the following skills :

¿ Mechanics : to parameterize a moving solid in the space; To apply the Newton¿s laws to moving solids.

¿ Introduction to numerical modelling : to model simple problems using PDEs; to analyse stability and consistency of a finite difference scheme; to program with Python a finite difference scheme or the Monte-Carlo method for solving a linear parabolic PDE; to analyse numerical results and identify / explain numerical errors.

¿ Modelling project : to develop a solution to the initial engineering problem by employing the different mathematical and numerical tools studied in his other courses.

Pré-requis

Required knowledge for each subject :

¿ Mechanics : mathematics (derivation, intégration, PDE), atomic structure , point mass mechanics.

¿ Introduction to numerical modelling : basis of probability theory, of integral and differential calculus, and of numerical analysis.

¿ Modelling project : numerical analysis, matrix computations, optimisation, ODE, PDE, geometrical modelling, probabilities, statistics, programming (Python).

Évaluation

L’évaluation des acquis d’apprentissage est réalisée en continu tout le long du semestre. En fonction des enseignements, elle peut prendre différentes formes : examen écrit, oral, compte-rendu, rapport écrit, évaluation par les pairs…