Isogeometric analysis for electromagnetic scattering problems

This paper is about the solution of electromagnetic scattering, when the scatterer is a conductor. The related equations are of integro-differential type and their fast discretization is a real challenge in numerical analysis. These equations depend on the frequency, and they lack stability at both high and low frequencies: any good numerical method has to cope with these instabilities. We will introduce suitable approximation techniques based on splines, see [1], and discuss how this could be used to improve on the state of the art in electromagnetic scattering problems. In particular, we will show how the use of splines allows to establish efficient Calderón-based preconditioners for high order discretizations.