V.V. Akhiyarov

In this paper the diffraction problems solution using parabolic equation (PE) is considered. Mathematically rigorous transition from Helmholtz equation to the parabolic equation and forward propagation is presented. Two ways of the differential operator approximation are produced; also various ways of the terrain representation and corresponding PE are shown. It is obtained that the staircase terrain approximation gives the results, completely corresponding with analytical solutions. An algorithm for the diffraction problems numerical solution, taking into account backward scattering, is produced. For the wedge diffraction problem it is shown that if the terrain is very rough, one should consider the backward scattering. The algorithm, taking into account backscattering, provides an opportunity to solve scalar diffraction problem for the arbitrary cross-section cylinder with Dirichlet boundary conditions. In free space PE has an analytical solution and so it gives possibility for the reflection suppressing from the computational domain boundaries into perfectly-matched layer. The real part of the scattered field for the circular and square cross sections cylinders is shown. RCS calculation method based on near field integration technique shows that the RCS in forward direction agrees with integral equation method.