Application of mosaic-skeleton approximations of matrices in the physical optics method for electromagnetic scattering problems

The paper considers a physical optics model based on the Kirchhoff–MacDonald approximation taking into account re-reflections for solving electromagnetic-wave scattering problems. This model uses an integral representation of the electromagnetic field via surface currents. The paper describes an iterative algorithm in which, at each iteration step, the surface currents on the surface partition cells is determined by multiplying the influence matrix by the currents found at the previous iteration. To increase the computational efficiency of the algorithm, the influence matrix is compressed using the method of mosaic-skeleton approximations. In this case, the specificity of the matrix being approximated is taken into account by determining its elements via the matrix of the discrete representation of the integral operator, which contains the matrix of “visibility” of the partition cells. The visibility matrix indicates whether the segment connecting the centers of two cells intersects the illuminated surface at its internal points. The method was tested on model problems, which showed the applicability of the proposed algorithm to solving the problems of scattering by non-convex bodies, as well as the computational efficiency of the algorithm.