The method of parametric representations of integral and pseudo-differential operators in diffraction problems on electrodynamic structures

Mathematical models of 2D electrodynamic wave diffraction and 3D scalar diffraction problems are the external boundary-value problems for the Helmholtz equation with boundary conditions of the first, second or third kind on the boundary surfaces. One of the effective ways of solving these boundary-value problems consists in their reduction to a singular and hypersingular boundary integral equations by the method of parametric representations of integral and pseudo-differential operators. The numerical solution of integral equations is obtained by using the modifications of discrete singularities method. The reasoning in applying this approach to constructing mathematical models of wave diffraction problems had been discussed.