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A numerical technique for solving scattering problems is presented. It is\ud based on a boundary integral equation idea, so the unknowns are localized on the contour (in 2D case) or the surface (in 3D case) of the scattering object. Two major difficulties of traditional boundary integral methods (the appearance of spurious resonances and the necessity to perform numerical integration of singular functions) are overcome by studying the problem in an approximate discrete formulation from the very beginning. The space is filled by cubic blocks, and the shape of the scatterer is formed by a set of blocks removed from the space. Thus, the formulation of the problem is discrete and the continuous Green’s function is substituted by a discrete mesh Green’s function. An analogue of combined field boundary integral equation (CFIE) is developed for this formulation.Postprint (author’s final draft

Abstract-A new numerical method for solving wave diffraction problems is given. The method is based on the concept of boundary elements; i.e., the unknown values are the field values on the surface of the scatterer. An analog of a boundary element method rather than a numerical approximation of the initial (continuous) problem is constructed for an approximate statement of the problem on the discrete lattice. Although it reduces the accuracy of the method, it helps to simplify the implementa tion significantly since the Green functions of the problem are no longer singular. In order to ensure the solution to the diffraction problem is unique (i.e., to suppress fictitious resonances), a new method is constructed similarly to the CFIE approach developed for the classical boundary element method.

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Recently, a new technique has been proposed by one of the authors for solving diffraction problems belonging to certain class. The class includes 2D problems that can be reduced to propagation problems on branched surfaces by applying the method of images. One of the simplest problems belonging to this class is diffraction by an infinitely thin ideal strip. Within the framework of the new method, a "spectral equation" is derived, which is an ordinary differential equation for the components of the directivity of the scattered field. The coefficients of the spectral equation are known up to several numerical parameters, and these are found by a complicated numerical procedure from the a-priori known monodromy data for the equation. In the current paper the numerical procedure is described and its accuracy and efficiency are analyzed.