Two Approaches to Solving the Problem of Plane Wave Diffraction by a Doubly Periodic Rough Surface

Modified discrete source method and diagram equation method are used to develop two algorithms for solving a three-dimensional scattering problem in the case of scattering from an acoustically soft or acoustically hard doubly periodic rough surface. Calculations use the efficient algorithm developed earlier for determining a periodic Green’s function in the problem of diffraction by a grating consisting of bodies of revolution. For the algorithm based on the diagram equation method, applicability conditions are determined. The two methods are compared in application to a sine-shaped doubly periodic surface. Fulfillment of both the energy conservation law and the boundary condition at the central surface element is verified. Dependences of reflected harmonic amplitudes on wave parameter and angle of incidence of plane waves are plotted.