Effective algorithms for modeling 3-D wave scattering problems on transparent structures

The method of volume integral equations (VIEs) is one of the most advanced and efficient techniques for numerical solution of scattering problems on 3-D transparent structures. By using the collocation method and taking into account that the kernel of integral equations depend only on the difference of arguments we reduce VIE to a system of linear algebraic equations (SLAE) with the matrix having special symmetry properties. Matrix-vector multiplication is the most laborious operation when iteration techniques are applied. Using discrete fast Fourier transform techniques we construct a fast algorithm for the multiplication of the SLAE matrix and the vector. We obtain estimations for parameters T (number of arithmetic operations necessary for matrix-vector multiplication) and M (memory volume required for implementation of the algorithm) that govern the efficiency of a numerical algorithm.