2023-2024 / MATH0471-2

Multiphysics integrated computational project


33h Th, 30h Proj.

Number of credits

 Master of Science (MSc) in Biomedical Engineering5 crédits 


Romain Boman, Christophe Geuzaine

Language(s) of instruction

English language

Organisation and examination

All year long, with partial in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit 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 project. 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 project. 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 learning unit

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.

This course contributes to the learning outcomes I.1, I.2, II.1, II.2, II.3, III.1, III.2, III.3, III.4, IV.1, IV.2, VI.1, VI.2, VI.3, VI.4, VII.2, VII.3, VII.4, VII.5 of the MSc in biomedical engineering.

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, hybrid learning)


Recommended or required readings

Cf. course website.

Written group project report and oral presentation.
The final evaluation is mandatory during the first exam session, and cannot be postponed to the second exam session.

Work placement(s)

Organisational remarks and main changes to the course


Prof. C. Geuzaine (cgeuzaine@uliege.be) et Dr. R. Boman (r.boman@uliege.be)


Association of one or more MOOCs