Classes

A new class for graduate students (e.g., master program in CES, SiSc, Math, Physics, etc) on development of modern numerical software for simulation of complex engineering problems. The course is recommended for master students.

A link to the RWTHOnline entry for the course will be provided soon.

Goals and topics

In this course, advanced numerical methods for solving PDEs are presented and discussed, along with aspects of efficient numerical software design, focusing on robustness, accuracy in large-scale simulations, as well as reproducible research. Students gain insight into how modern simulation software is designed, implemented, and validated for real-world scientific and engineering applications. The associated exercises will focus on the practical application of open-source frameworks implementing these methods. Topics include (among others) finite element and discontinuous Galerkin methods, iterative solvers, particle-based methods, and an introduction to uncertainty quantification.

Info

The formal structure of the class will be 2 hour of lectures and 1 hour of tutorial each week. The tutorials will be merged into 2 hours every alternating week.

There are 5 ECTS points to earn with the exact examination form (oral exam or evaluation based on applied project work throughout the semester) to be decided by the start of the course.

See also online.rwth-aachen.de. Please register with the course to gain access to the Moodle-Page.

Some Background Literature

The course is a combination of several topics and there is no single book which it can be based on. Moreover, some of the material is quite recent and might be not well represented in books; however, the books listed should provide a good overview of the fundamentals used throughout the whole course.

• D. A. Kopriva (2009). Implementing spectral methods for partial differential equations: Algorithms for scientists and engineers. Springer Science & Business Media.
• Logg, A., Mardal, K. A., & Wells, G. (Eds.). (2012). Automated solution of differential equations by the finite element method: The FEniCS book (Vol. 84). Springer Science & Business Media.
• R. C. Smith (2024). Uncertainty Quantification: Theory, Implementation, and Applications. SIAM Computational Science and Engineering Series.
• I.D. Boyd, T.E. Schwartzentruber (2017). Nonequilibrium gas dynamics and molecular simulation. Cambridge University Press