Решение двумерной задачи дифракции волн на фракталоподобных телах методом диаграммных уравнений

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The solution of the two-dimensional wave diffraction problem for infinite cylinder of complex cross-section was considered by using the pattern equations method (PEM). A triangle and a Koch snowflake of first iteration were chosen as the geometry of the cross-sections of the cylinder. The numerical algorithms of the PEM for a single scatterer and for a group of bodies with the Dirichlet condition on their boundary are briefly presented, and the results of numerical calculations of the scattering characteristics for the above geometries are obtained using the PEM and the method of continued boundary conditions (MCBC). To check the convergence of the numerical algorithm in both methods, the optical theorem was used. The limits of applicability of the PEM for fractal scatterers are established. It is shown that for all convex bodies the algorithm of the PEM is sufficiently stable and allows obtaining calculation results with an accuracy acceptable in practice. In the case of a non-convex body, namely, a Koch snowflake, the algorithm of the PEM for a single scatterer turns out to be unstable and the acceptable accuracy can be obtained only if this geometry is considered as a group of bodies composed of convex geometries (for example, triangles).