Boundary Integral Equation and the Problem of Diffraction by a Curved Surface for the Parabolic Equation of Diffraction Theory

Abstract

The 2D problem of diffraction by a curved surface with ideal boundary conditions is considered in terms of the parabolic equation of diffraction theory. A boundary integral equation of Volterra type in Cartesian coordinates is introduced. Using the latter, the problem of diffraction by a parabola is analyzed. It is shown that the solution of this problem coincides with the asymptotic solution for the problem of diffraction by a cylinder obtained by V. A. Fock. The Efficiency of the numerical solution of the boundary integral equation is demonstrated for diffraction on a perturbation of a straight boundary.