Regularization techniques for the singular integral operators in the wave diffraction theory

The integral equations typically possess singular kernels. Some preliminary analytical regularization is performed before their numerical treatment. The universal and effective direct numerical solution of singular integral equations with the Cauchy type kernels is a well known technique in fracture mechanics. Traditional one-dimensional contour integral equations derived in the scalar diffraction theory are not of such a class. They either possess logarithmic singularity or contain integrals in the finite part sense according to Hadamard. The fields appear during the electromagnetic wave diffraction on the system of cylindrical objects with different properties. Those objects could be perfectly conducting shells and screens, dielectrics, thin absorbed or dielectric films, finite-conducting bodies. Neither the shape of the structure nor cross-section, no position of its elements is bounded by the considered approach. The developed method can be applied in a wide frequency range.