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Numerical analysis - 4PMNNUM9

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  • Number of hours

    • Lectures : 15.0
    • Tutorials : 15.0
    • Laboratory works : 30.0
    • Projects : ?
    • Internship : ?
    ECTS : 4.0

Goals

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

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.

Tests



Additional Information

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

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Date of update February 26, 2019

Grenoble INP Institut d'ingénierie Univ. Grenoble Alpes