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Geometrical transformations and equivalent materials in computational electromagnetism

A. Nicolet (Faculté de Saint‐Jérôme, Institut Fresnel, Université Aix‐Marseille, Marseille, France)
F. Zolla (Faculté de Saint‐Jérôme, Institut Fresnel, Université Aix‐Marseille, Marseille, France)
Y. Ould Agha (Faculté de Saint‐Jérôme, Institut Fresnel, Université Aix‐Marseille, Marseille, France)
S. Guenneau (Department of Mathematical Sciences, University of Liverpool, Liverpool, UK)

Abstract

Purpose

This paper aims to review various techniques used in computational electromagnetism such as the treatment of open problems, helicoidal geometries and the design of arbitrarily shaped invisibility cloaks. This seemingly heterogeneous list is unified by the concept of geometrical transformation that leads to equivalent materials. The practical set‐up is conveniently effected via the finite element method.

Design/methodology/approach

The change of coordinates is completely encapsulated in the material properties.

Findings

The most significant examples are the simple 2D treatment of helicoidal geometries and the design of arbitrarily shaped invisibility cloaks.

Originality/value

The paper provides a unifying point of view, bridging several techniques in electromagnetism.

Keywords

Citation

Nicolet, A., Zolla, F., Ould Agha, Y. and Guenneau, S. (2008), "Geometrical transformations and equivalent materials in computational electromagnetism", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 4, pp. 806-819. https://doi.org/10.1108/03321640810878216

Publisher

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Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited