Centre de Mathématiques et de Leurs Applications

Jeudi 24 Janvier 2008

Orateur : Ning Yan Zhu (université de Stuttgart) & M.A. Lyalinov (université de St Petersbourg)

Titre : Diffraction of acoustic and electromagnetic waves by impedance wedge and cones

Résumé : This report is centred on some recent advances in wave diffraction bytwo classes of canonical structures: wedge-shaped regions and conical bodies of circular cross section.

The first step of the solution procedure consists in deducing certainsecond-order functional difference equations (SOFDEs) from the the impedance-type boundary conditions to be satisfied on the surfaces of the canonical structures, by making use of the Sommerfeld-Malyuzhinets technique for wedge-shape regions and Kontorovich-Lebedev transform for conical bodies. In the second step the SOFDEs are to be simplified by either the generalised Malyuzhinets function or a special function introduced by Bernard. By the aid of the so-called S-integrals the equivalence of the simplified FDEs and an integral expression is then established, with the integration in the latter extends over the imaginary axis of a complex plane. Precisely for complex variables on the imaginary axis does the integral expression become a Fredholm integral equation of the second kind, which admits an efficient numerical solution via for instance quadrature method. With the so obtained spectra, the looked-for fields are determined, and the far-field representations follow from an asymptotic evaluation of the integrals.

Both the theoretical and the numerical sides will be discussed in this report. Typical behaviour of wave diffraction by these two classes of canonical structures will also be shown.