Isogeometric Analysis provides a natural connection between CAD and numerical simulation by using smooth spline-based functions to represent both the geometry and the unknown fields. However, its application to complex geometries is still limited by the need for analysis-suitable, body-fitted discretizations. Immersed methods offer an alternative route by embedding the physical domain into a simpler background discretization, reducing the dependence on mesh generation and geometrical preprocessing.

This seminar will present a set of immersed isogeometric techniques developed to address these challenges, with particular focus on the Shifted Boundary Method, the Gap-Shifted Boundary Method, and their extension to non-conforming multipatch coupling. The standard Shifted Boundary Method avoids cut-cell integration by replacing the true physical boundary with a mesh-aligned surrogate boundary and transferring boundary conditions through Taylor-based shift operators. This provides a robust and well-conditioned framework for embedded isogeometric analysis.

The Gap-Shifted Boundary Method extends this idea by reconstructing the geometrical region between the surrogate and physical boundaries and using it only for numerical integration, without introducing additional degrees of freedom. This improves the treatment of traction-dominated problems and provides a natural framework for more general immersed isogeometric formulations. The same gap-reconstruction concept can also be used for multipatch coupling, enabling non-matching parametrizations, arbitrary local refinement, and flexible coupling between independently discretized patches.

The main objective of the seminar is to illustrate the potential of these methods as building blocks for robust and automation-friendly CAD-to-analysis workflows. Structural mechanics and contact mechanics will be used as representative application fields to highlight the role of high-order spline discretizations, boundary treatment, local refinement, and interface handling. Numerical examples will include embedded structural benchmarks, multipatch configurations, and frictionless contact problems, showing how SBM and Gap-SBM can be used to address different levels of geometrical and mechanical complexity.