Geometrical transformations and equivalent materials in computational electromagnetism

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.

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

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

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