---
author:
- |
    Abele Simona $^{(1),(2)}$, Luca Bonaventura$^ {(1)}$\
    Carlo de Falco $^{(1)}$, Sebastian Schöps $^{(2)}$
bibliography:
- 'axis\_iga.bib'
title: IsoGeometric Approximations for Electromagnetic Problems in Axisymmetric Domains
---

\(1) MOX – Modelling and Scientific Computing,\
Dipartimento di Matematica, Politecnico di Milano\
Via Bonardi 9, 20133 Milano, Italy\
[abele.simona@polimi.it, luca.bonaventura@polimi.it, carlo.defalco@gmail.com ]{}\
[$ \ \ $ ]{}\
(2) Technische Universität Darmstadt\
Centre for Computational Engineering\
Dolivostra[ß]{}e 15, 64293 Darmstadt, Germany\
[abele@gsc.tu-darmstadt.de, schoeps@gsc.tu-darmstadt.de ]{}\

[**Keywords**]{}: Electromagnetic Fields, Maxwell Equations, IsoGeometric Analysis, Axisymmetric Domains, De Rham Complexes

[**AMS Subject Classification**]{}: 65L05, 65P10, 65Z05, 70G65, 78A35

Introduction {#intro}
============

The solution of the Maxwell equations on axisymmetric domains, as the one depicted in Figure \[fig:axis\_scheme\], plays an important role in many applications, such as, for example, electrical machines, cables, the beam pipe of a particle accelerator magnet or resonating cavities.

![Representation of a cross-section $\srfdomflat$ lying on the $\parGs{\rho=0}$ axis (right) and its associated axisymmetric domain $\voldomaxis$ (right). $\Gamma_0$ represents the portion of the boundary of $\srfdomflat$ on the axis.[]{data-label="fig:axis_scheme"}](img/pin_head/axis_scheme){width="75.00000%"}

Several tailored numerical techniques to solve electromagnetic problems on such domains have been proposed in the literature, *e.g.*, among many others, [@assous:2002; @bernardi:1999; @borm:2002; @copeland:2006; @copeland:2010; @gopalakrishnan:2012; @li:2011; @mercier:1982; @oh:2015]. In particular, 