Multiphysics integrated computational project

In this course, students work in groups to develop a scientific computing code to solve one or more partial differential equations describing a physical phenomenon.

The numerical methods used are chosen according to the physical problem under study: the emphasis is placed on the mathematical properties of the methods, the specifics of their computer implementation, and their practical use on a computer (compilation, debugging, analysis, and visualization of results).

The code is developed in a compiled language (C/C++), with great importance given to source code clarity, modularity, and efficiency (potentially in parallel). This code is then used to analyze both the numerical behavior of the methods (convergence, stability, etc.) and the physics of the modeled phenomena (parameter variations, changes in assumptions, etc.).

A few examples of physical problems addressed in recent years include: current penetration in a superconductor, thermo-mechanical coupling in a microsystem, dielectric heating of human skin, traffic flow simulation, wave propagation in an infinite medium, tsunami modeling, microfluidics simulation, and more.

Examples of numerical methods studied include: finite differences, finite elements, discontinuous Galerkin methods, boundary elements, finite volumes, semi-analytical methods, and particle methods.

In this course, students work in groups to develop a scientific computing code to solve one or more partial differential equations describing a physical phenomenon.

The numerical methods used are chosen according to the physical problem under study: the emphasis is placed on the mathematical properties of the methods, the specifics of their computer implementation, and their practical use on a computer (compilation, debugging, analysis, and visualization of results).

The code is developed in a compiled language (C/C++), with great importance given to source code clarity, modularity, and efficiency (potentially in parallel). This code is then used to analyze both the numerical behavior of the methods (convergence, stability, etc.) and the physics of the modeled phenomena (parameter variations, changes in assumptions, etc.).

A few examples of physical problems addressed in recent years include: current penetration in a superconductor, thermo-mechanical coupling in a microsystem, dielectric heating of human skin, traffic flow simulation, wave propagation in an infinite medium, tsunami modeling, microfluidics simulation, and more.

Examples of numerical methods studied include: finite differences, finite elements, discontinuous Galerkin methods, boundary elements, finite volumes, semi-analytical methods, and particle methods.

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.

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.

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

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

Theoretical lectures and group project.

Theoretical lectures and group project.

Face-to-face

Face-to-face

Cf. course website.

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.
 

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.
 

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

 

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