Abstract <p>The paper considers algorithms for solving problems of electromagnetic wave scattering in the frequency domain using the method of integral equations, as well as using the physical optics model taking into account a multiple reflected field. In both cases, the main computational costs, both in terms of computation time and in terms of the required computer memory, are associated with storing dense matrices of interaction of discrete elements and performing operations with these matrices. The features of applying the method of mosaic-skeleton approximations to such matrices, and the capabilities of this method in this class of problems are analyzed.</p>