Isogeometric Analysis (IGA) is a finite-element-type method that uses the same basis functions to represent the solution (e.g., displacement field) and to describe the geometry of the problem domain. This integration allows for a an accurate representation of the geometry and can lead to improved convergence rates in numerical simulations compared to traditional methods that use separate representations for the geometry and solution spaces. It has been applied to various fields, including solid mechanics, fluid dynamics and electromagnetics. In the context of the project CREATOR it has proven advantageous for the simulation of rotating electric machines. Therefore an Autumn School with this topic was organised in November 2024, which was open to all affiliates of CREATOR.

9:00-09:45 Florian Feppon (KU Leuven)

Towards multiscale topology optimization of fluid devices with the homogenization method: numerical and theoretical developments

09:45-10:15 Kamran Sadiq (RICAM)

On a two dimensional inverse source problem in scattering medium with partial boundary data

10:15-10:45 Soumen Senapati (RICAM)

Reconstruction of acoustic medium properties and source in time-domain by injecting contrasting agents

11:00-11:30 Nepomuk Krenn (RICAM)

Topology optimization of a permanent magnet synchronous machine by the topological derivative

11:30-12:00 Peter Gangl (RICAM)

Homotopy methods for higher order shape optimization

The goal of this workshop is to bring together scientists from numerical analysis, geometric modeling and engineering who are interested in topology optimization and isogeometric analysis. We aim at connecting the two fields by developing an isogeometric modeling framework that is well-suited for topology optimization, i.e., that allows for general topologies and that can handle changes in the topology in a robust and efficient way. On the other hand, we study topology optimization technologies that are suitable for B-spline and NURBS based geometry discretizations. The topics of the talks range from topology optimization in practical applications, topological derivatives, level set and density-based methods, to geometric modeling of topologically complex shapes, geometry segmentation and parametrization methods and unstructured splines spaces.

The goal of this mini-workshop is to bring together experts from both mathematics and (electrical) engineering working on topics related to modeling, simulation and optimization of electric machines in either academia or industry. The workshop aims at providing a basic understanding of tools and workflows used in industry and at identifying challenges and common topics of interest. We plan to have a loose atmosphere and encourage discussion at any time during presentations.