Multi-scale modeling of the time-harmonic scattering from a thin layer of randomly distributed small particles

We consider the time-harmonic scattering problem of an electromagnetic plane wave from a multilayer coated PEC object covered with an additional very thin layer made up of a large number of randomly distributed PEC particles. Because the size of the particles is very small compared with the wavelength of the incident wave and the multilayer thickness, the solution cost of Maxwell’s equations is considerably reduced if the multilayer coating is replaced on its outer boundary Σ
0
by the standard impedance boundary condition (SIBC) and the particles layer is replaced by an appropriate IBC prescribed on a surface Σ
H
located above. This IBC is obtained via an asymptotic analysis by considering the scattering problem from the infinite planar surface Σ
0
coated with the particles. We consider here the Helmholtz equation (2-D problem) with two configurations: a periodic distribution and a random one. Various numerical examples highlight the IBC efficiency.