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In this paper we introduce methods for electromagnetic wave propagation,based on splines and on T-splines. We define spline spaces which form a De Rhamcomplex and, following the isogeometric paradigm, we map them on domains whichare (piecewise) spline or NURBS geometries. We analyse their geometricstructure, as related to the connectivity of the underlying mesh, and we give aphysical interpretation of the fields degrees-of-freedom through the concept ofcontrol fields. The theory is then extended to the case of meshes withT-junctions, leveraging on the recent theory of T-splines. The use of T-splinesenhance our spline methods with local refinement capability and numerical testsshow the efficiency and the accuracy of the techniques we propose.

Isogeometric Methods for Computational Electromagnetics: B-spline and T-spline discretizations