Problem of designing an aerodynamic profile with assigned characteristics of electromagnetic scattering

Abstract

At the profile trailing edge, the Joukowski–Chaplygin condition is posed that expresses the finiteness of the velocity at the flow trailing point. The inverse problem for the reconstruction of the unknown profile-surface segment S0 ⊆ S is considered in the following formulation. It is necessary to find a set of values ri, i = 1, 2, ..., L, which parametrically determine the desired surface segment S0 and provide: (i) approximation (at a reasonable level of accuracy) to the prescribed scattering diagram; (ii) shock-free incoming flow around the profile (streamline flow around the profile leading edge). We now assume that the scattering diagram is given by its complex values at a finite number of far-field points: ea(φ), φ ∈ {φj, j = 1, 2, ..., m}; φ is the polar angle; 2m = L – 1 [for H-polarization, the function ha(φ) is given]. The criterion of the approximation to the given scattering diagram (in the mean-square sense) is