Peculiarities of the boundary integral equation method in the problem of electromagnetic wave scattering on ideally conducting bodies of small thickness

Abstract

The method of boundary integral equations with hypersingular integrals is used for the numerical solution of the classical problem of electromagnetic wave scattering on ideally conducting bodies. The corresponding integral equations are solved by the methods of piecewise constant approximations and collocation. As a result, the problem is reduced to a system of linear algebraic equations whose coefficients are expressed in terms of integrals over partition cells with a strong power singularity. These integrals are evaluated using the previously developed approach based on the extraction of terms with a strong singularity calculated analytically. The proposed numerical scheme based on the calculation of the remaining terms with weakly singular integrals over partition cells is performed by constructing a fine grid of second level with multiplication of the integrands on a smoothing factor is tested. By the example of scattering on a rectangular it is shown, in particular, that this scheme allows one to solve the scattering problem on bodies of small thickness. In this case, the thickness of a body may be less then the diameter of the first level cells. However, the diameter of the second level cells must be much less than the thickness of the body.