MATH0471-2 : Multiphysics integrated computational project

Study Programmes 2015-2016

MATH0471-2

Multiphysics integrated computational project

Duration :

20h Th, 30h Proj.

Number of credits :

Master in biomedical engineering (120 ECTS)		5
Master in mechanical engineering (120 ECTS)		5

Lecturer :

Romain Boman, Christophe Geuzaine

Language(s) of instruction :

English language

Organisation and examination :

All year long, with partial in January

Units courses prerequisite and corequisite :

Prerequisite or corequisite units are presented within each program

Course contents :

In this course the students develop a scientific computing code to solve partial differential equations describing physical phenomena.
The course is organized in two parts: theoretical lectures and a group project.
The theoretical lectures remind (or introduce, if needed) the numerical method(s) necessary for the completion of the projects. The focus is on the mathematical properties of the methods and on their practical computer implementation (compilation, debugging, analysis and visualization of the results).
The projects are carried out in groups of variable size, depending on their complexity. The computer code is developped in a compiled language (usually C or C++), with emphasis put on the clarity of the source code, its modularity and its efficiency (potentially in parallel). The software is then used to analyse the numerical bahaviour of the methods and the physical behaviour of the studied phenomena (under parameter and hypothesis change, etc.).
Table of contents:

Reminder and theory (convergence, stability) of the numerical methods to be used in the projects. Some examples studied in the previous years : finite difference, finite elements (continuous and discontinuous), finite volumes, semi-analytical methods, explicit and implicit time integrators, etc.
Introduction to development tools
Project. Some examples solved during the last few years: current penetration in superconductors, thermomechanical coupling in microsystems, dielectric heating of the huma skin, traffic congestion modeling, wave propagation in infinite media, tsunami modeling, ...

Learning outcomes of the course :

By the end of the course the students will have carefully studied a numerical technique for the solution of partial differential equations, both at the mathematical and at the computational level. They will have put into practice the knowledge acquired during courses on mathematical analysis, numerical analysis, partial differential equations and high performance scientific computing, by applying them to a concrete physical problem.
The course serves as a preparation to engineering numerical modelling, both in industry and in academia. It leads students to question the correct use of numerical simulation tools.

Prerequisite knowledge and skills :

Courses on mathematical and numerical analysis, on partial differential equations, and on high performance scientific computing.

Planned learning activities and teaching methods :

Theoretical lectures and group project.

Mode of delivery (face-to-face ; distance-learning) :

Face-to-face