Special Topics in Computational Science and Engineering

The course discusses the state-of-the-art of a selected topic from computational science and engineering. This topic changes yearly. The first part of the course gives an introduction to the subject through lectures in Q3. In the second part of the course (Q4), students will carry out a project to apply the theory and methods taught in the first part.

The topic of the course in the academic year 2025/2026 is Geometry + Simulation in Isogeometric Analysis. It will given by Matthias Möller, Stefanie Elgeti, Ye Ji and Jingya Li.

Isogeometric Analysis (IGA) is a computational methodology that integrates Computer-Aided Design (CAD) and Finite Element Analysis (FEA) by using spline-based functions (such as Bsplines and NURBS) for both geometry representation and numerical simulation. This approach offers increased accuracy and smoothness, especially in problems where higher-order continuity is essential. Over the past decade, IGA has found applications in fluid and solid mechanics, multi-physics coupling, and shape and topology optimization.

This course introduces the fundamental concepts of IGA and its recent developments. It will also explore its integration with modern topics such as:

• isogeometric collocation methods,

• shape and topology optimization,

• nonlinear structural analysis, and

• machine learning techniques for geometry- and simulation-aware modeling.

• Students will also gain hands-on experience with open-source IGA tools (G+Smo, GeoPDEs, Nutils, splinepy based on their levels of programming).