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The Solution of Diffraction Problems by a Method of Elementary Scatterers


A.G. Kyurkchan, N.I. Smirnova

Pattern equation method (PEM) is widely used for solving diffraction problems. One of the PEM advantages is a weak dependence of the speed and accuracy of computational algorithm on the distance between single scatterers. This fact leads us to the idea of modeling scattering characteristics of complex geometry bodies by solving wave diffraction problems on two of more simple geometry bodies, which in the aggregate reproduce examined complex object. Calculations have showed the efficiency of such approach. Natural generalization of this idea is to substitute a scatterer with complex geometry and structure, for example a non homogeneous magneto-dielectric scatterer, by the group of simple homogeneous bodies, for example spheres (or circles in two dimensional case), which sizes are small in comparison to the wave length. In the article this idea is realized by the example of the solution of a two dimensional diffraction problem with Dirichlet boundary condition. Thus the most difficult is considered for the suggested approach a case of diffraction of waves on thin screens. Scatterer it is replaced with group of the circular cylinders located on its directing. Using typical for PEM technique we can reduce this problem to the infinite algebraic system relatively to Fourier expansion coefficients of cylinders scattering pattern. In article it is used one mode approximation at which Fourier series for the scattering pattern of each cylinder is reduced to one composed. The algebraic system thus has extremely simple kind. Examples of the solution by suggested way of diffraction problems on screens as a flat strip and a part of the circular cylinder are considered. It is shown, that the suggested approach allows to carry out with graphic accuracy calculations of scattering characteristics of thin screens with the minimal expenses of computing resources.

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