Isogeometric analysis (IGA) offers superior accuracy in numerical simulations compared to the classical finite element method due to its exact representation of geometry through smooth spline functions such as B-splines and NURBS. However, automating mesh generation for IGA on complex geometries is a challenge. Thus, alternative techniques such as fictitious domain methods have been introduced, in which the geometry is immersed into a Cartesian grid and only the quadrature rule, but not the basis functions, are adapted to the geometry. The combination of these methods with IGA results in immersed isogeometric analysis (immersed IGA), a promising approach known for its high convergence rates and efficient integration schemes, such as the boundary-conformal quadrature (BCQ) method. This synergy between immersed IGA and BCQ has demonstrated robustness in various applications, including linear elasticity, thermo-elasticity, and large deformation elasticity.

Potential topics

• Develop and implement immersed IGA with boundary-conformal quadrature in the context of coupled magnetic, thermal and elastic field problems
• Extend the immersed IGA with boundary-conformal quadrature to parametric and shape optimization with gradient based optimization methods