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

TL;DR

This paper develops isogeometric discretization methods for electromagnetic wave propagation using B-splines and T-splines, emphasizing geometric structure, local refinement, and physical interpretation of degrees of freedom.

Contribution

It introduces spline and T-spline based methods for electromagnetics that form a De Rham complex and extend to T-junction meshes, with analysis and physical interpretation.

Findings

Methods demonstrate high accuracy in numerical tests

T-splines enable local mesh refinement

The approach maintains physical consistency of electromagnetic fields

Abstract

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 Rham complex and, following the isogeometric paradigm, we map them on domains which are (piecewise) spline or NURBS geometries. We analyse their geometric structure, as related to the connectivity of the underlying mesh, and we give a physical interpretation of the fields degrees-of-freedom through the concept of control fields. The theory is then extended to the case of meshes with T-junctions, leveraging on the recent theory of T-splines. The use of T-splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose.