This lecture presents isogeometric analysis (IGA) in the context of electromagnetic simulations, . IGA extends the set of polynomial basis functions, commonly employed by the classical Finite Element Method (FEM). While identical to FEM with Nedelec's basis functions in the lowest order case, it is generally based on B-spline and Non-Uniform Rational B-spline basis functions. The main benefit of this extension is the exact representation of the geometry in the language of computer aided design (CAD) tools. This simplifies the meshing as the computational mesh is implicitly created by the engineer using a CAD tool.
The lecture starts with an introduction into electromagnetic field theory and the curl- and div-conforming spline function spaces are discussed. Finally, several interesting benchmark examples are shown which are for example used in optimisation and uncertainty quantification workflows. A hands-on session will demonstrate the free software geoPDEs which implements all necessary function spaces in a Matlab of GNU Octave environment.
 Zeger Bontinck, Jacopo Corno, Herbert De Gersem, Stefan Kurz, Andreas Pels, Sebastian Schöps, Felix Wolf, Carlo de Falco, Jürgen Dölz, Rafael Vázquez, and Ulrich Römer. “Recent Advances of Isogeometric Analysis in Computational Electromagnetics”. In: ICS Newsletter (International Compumag Society) 3 (Nov. 2017). URL: https://arxiv.org/abs/1709.06004.