Numerical methods

Numerical Methods for PDEs:Finite difference discretization of partial differential equations (stationary and time dependent problems); solution of very large linear systems (direct and iterative methods, including multigrid methods); rounding errors, numerical stability and control of the accuracy.

Monte Carlo Methods: Relevance of Monte Carlo simulation. Estimation of definite integrals. Convergence and accuracy. Variance-reduction methods. Application to particle transport problems and to system reliability

Project: Dévelopment of an individual project.

Numerical Methods for PDEs: Learn modern techniques to numerically solve partial differential equations.

Monte Carlo Methods: Introduction to Monte Carlo simulation, to the statistical convergence of the algorithms, to variance-reduction techniques...

Project:Learn to solve a numerical problem with a program written in an adapted langage (C or Fortran).

Numerical Methods for PDEs: Commented slides + live questions & answers and exercise sessions.

Monte Carlo Methods: ex-cathedra and collaborative lectures; exercises

Project:Learning by projet.

Contribution to the teaching profile

Solution of technical and scientific problems:

- by using the knowledge acquired during the course (PE1);

- by using rigorous and creative approaches (PE2);

Preparation of a technical report followed by an oral defense of the project (PE5)

References, bibliography, and recommended reading

cf. Université Virtuelle

Course notes

• Podcast
• Université virtuelle

Contacts

Solbosch, Build. D, Level 3, entrance B:

Yvan Notay: room 156 ; Phone : +32 2 650 36 70 ; e-mail : ynotay@ulb.ac.be

Artem Napov: room 141 ; Phone : +32 2 650 20 70 ; e-mail : anapov@ulb.ac.be

Campus

Solbosch

Method(s) of evaluation

• Other

Other

Numerical Methods for PDEs: Written exam with documents.

Monte-Carlo Methods: Oral exam.

Project: Project evaluation based on the report, the software code, and the oral defense.

Mark calculation method (including weighting of intermediary marks)

Standard rule: 2/5 mark exam Numerical Methods for PDEs + 1/5 mark exam Monte Carlo Methods + 2/5 mark Project.

To benefit from the standard rule, either the three partial marks must be greater than or equal to 10, or two of them must be greater than or equal to 12 and the last equal to 9. In any other case, the minimum partial mark becomes the final one. Partial marks greater than or equal to 10 remain acquired for subsequent sessions.

Language(s) of evaluation

• english
• (if applicable french )