In the week October 13–17, 2025, researchers from across Europe came to the Johann Radon Institute for Computational and Applied Mathematics (RICAM) at the Campus of Johannes Kepler University (JKU) in Linz, Austria, to discuss recent advances in Isogeometric Analysis with possible applications to the simulation of Electric Machines.
One of the original visions of Isogeometric Analysis (IgA) was to bridge the gap between computer aided design (CAD) and finite element simulation by using the geometry description from CAD also for the simulation. This obsoletes the need for meshing algorithms that provide a representation of the geometry in terms of triangular, tetrahedral or similar meshes used in standard finite element methods. Those algorithms might be expensive and usually introduce an additional contribution to the error. This advantage seems to be particularly pronounced in the context of shape optimization (like for finding the optimal design of an electrical machinge), where feeding the optimized geometries back to the CAD systems would be desired as well. Certainly, such a tight coupling of CAD and simulation also poses challenges. While IgA is based on parametrizations of the objects of interest, many CAD representations only provide parametrizations of the boundaries of these objects. Moreover, parametrizations from the CAD systems are often not as regular as desired for IgA simulations. During the workshop, several talks have addressed the issue of further reducing the gap between CAD and simulation.
In standard IgA, tensor-product spline functions are used to represent the approximate solution. As high-order functions, they allow for faster convergence, compared to standard low-order finite elements methods. Since the full approximation power for uniform grid sizes can only be archived if the solution is sufficiently regular, adaptive refinement is essential, even more than for low-order methods. Tensor-product spline constructions provide also other opportunities, like for the construction of arbitrarily smooth function spaces or the construction of function spaces that exactly satisfy the de Rham complex used for the variational formulation of Maxwell’s equations, but again pose challenges for efficient matrix assembly, handling of geometries with complex toplogies or the solving of the resulting algebraic systems.
Presentations addressing these issues and utilizing these opportunities and on many more topics with relevance for the simulation of electrical machines were delivered by emerging researchers and established experts, providing a unique opportunity to learn about the progress of research in different fields and to establish new collaborations.
