Phelma Formation 2022

Numerical analysis - 4PMNNUM9

  • Number of hours

    • Lectures 15.0
    • Projects 0
    • Tutorials 15.0
    • Internship 0
    • Laboratory works 30.0

    ECTS

    ECTS 3.0

Goal(s)

The students will learn to handle the most common numerical methods for solving ordinary differential equations (ODE) and partial differential equations (PDE) for computational analysis of physical phenomena.

Contact Jean-Christophe TOUSSAINT

Content(s)

units of 4h as lecture/excercises/computer lab)

Course presentation - Introduction to scientific modelling - Introduction to Matlab (computer lab, 4h)
Solving ODEs, discrete step methods (2h lecture, 2h excercise, 4h computer lab)
Numerical integration: Newton-Cotes, Gauss, polynomial interpolation (2h lecture, 2h excercise, 4h computer lab)
Resolution of linear systems (direct and iterative methods) and non-linear systems. (2h lecture, 2h lab)
Finite Difference Method: Implicit/explicit scheme, Von Neumann stability (2h lecture, 2h excercises, 8h computer lab)
Finite Element Method: Nodal / Edge Elements (4h lecture, 4h excercise, 12h computer lab)



Prerequisites

Lecture, exercises and computer lab are being held in the same computer room using workstations. Matlab will be used as programming language. Course language: French.

Test

At the end of each chapter, a 15' evaluation will be given.
These evaluations represent a maximum bonus of 2 points in the final grade.

Written exam of 3 hours in session 1
Course notes, course handouts, TD statements and TD answer keys allowed
All other documents are forbidden
College" calculators allowed

The grade for session 2 will replace the grade for session 1. The exam of the 2nd session may be an oral exam.

In case of an exam during a lockdown period, the evaluation will be done by a written exam of 3 hours, or by an oral exam by videoconference or will be replaced by a homework.



Evaluations par QCM à la fin de chaque chapitre : bonus de 2 points max
Examen écrit Session1 : DS1
Examen écrit Session 2 : DS2
N1 = DS1 + bonus
N2 = DS2 + bonus

Additional Information

Course list
Curriculum->IPhy->Semester 7

Bibliography

  • P. LASCAUX & R. THEODOR : "Analyse numérique appliquée à l'art de l'ingénieur", Edition Masson, 2 tomes
  • G. DHATT & G. TOUZOT : "Une présentation de la méthode des éléments finis", Edition Maloine S.A., 2ème édition 1984
  • B. LUCQUIN & O. PIRONNEAU : "Introduction au calcul scientifique", Edition Masson, 1996