Spectral equations for scattering by impedance polygons : properties and solutions
Résumé
The Sommerfeld-Maliuzhinets representation of fields is not limited to the study of the
diffraction by isolated impedance wedges, and we developed in [1]-[2] an analytical method
concerning the determination of spectral function for the scattering by impedance polygonal
object (convex or not). Our method is now quoted and used by other authors, as very recently
in [3] for semi-infinite impedance polygons with three edges, but other approaches exist.
They can be exact for cavities, for perfectly conducting object, or for specific geometries [4]-
[8], or give asymptotic [9] or iterative [10] reduction. Our approach has the advantage to give
rigorous analytical equations in complex plane, which apply for general impedance polygons
with finite, but also infinite faces without being limited to single wedge. For that, we consider
special features of single face expression of spectral function that we defined in [1]-[2],
which leads to exact functional difference equations, and Fredholm integral equations for
finite or infinite polygons that we detail here with novel properties. Existence and uniqueness
of solutions are analysed in an original manner, and approximate asymptotics are discussed.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)