Advanced Numerical Methods

Due to the COVID-19 crisis, the information below is subject to change, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).

5 credits

30.0 h + 30.0 h

Teacher(s)

Chatelain Philippe; Craeye Christophe (coordinator); Legat Vincent; Remacle Jean-François;

Language

English

Main themes

Integral Methods
Finite elements
Spectral and pseudo-spectral Methods
Error estimation, adaptivity, mesh generation
Techniques of resolution of large (non-)linear systems
Implementation data-processing: parallel calculation, use of the specialized libraries, techniques of numerical programming.

Aims

At the end of this learning unit, the student is able to :

In consideration of the reference table AA of the program"Masters degree in Mechanical Engineering", this course contributes to the development, to the acquisition and to the evaluation of the following experiences of learning:

AA1.1, AA1.2, AA1.3
AA2.2, AA2.3, AA2.4
AA3.1, AA3.3
AA6.1, AA6.4

Advanced numerical methods The requirements for the students are the following:

To select and to apply the right method for a given problem.
To evaluate the algorithmic complexity of a method.
To efficiently use the numerical available libraries (Lapack)
To provide an estimate of the error.
To evaluate the quality of a mesh for a given method.
To perform a calculation on a parallel architecture.
To program a simple integral method.
To program a method finite elements.
To solve in an iterative way of the (non-)linear large systems

Content

Integral Methods.
Finite elements.
Spectral and pseudo-spectral Methods.
Error estimation, adaptivity, mesh generation.
Techniques of resolution of large (non-)linear systems.
Implementation data-processing: parallel calculation, use of the specialized libraries, techniques of numerical programming.

Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

In the pratical organisation, a great importance will be given to collaborative projets. Flexibility will be emphazed in order to focus on a problem solving approach.

Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Exam.
Homeworks are also graded and the obtained marks contribute to the final grade. Note that a pass grade (> 10) has to be obtained at the exam for the homework grades to be accounted for.

Online resources

https://moodleucl.uclouvain.be/course/view.php?id=9491

Faculty or entity

MECA

Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme

Sigle

Credits

Prerequisites

Aims

Master [120] in Physical Engineering

FYAP2M

Master [120] in Electrical Engineering

ELEC2M

Master [120] in Electro-mechanical Engineering

ELME2M

Master [120] in Mathematical Engineering

MAP2M

Master [120] in Biomedical Engineering

GBIO2M

Master [120] in Mechanical Engineering

MECA2M