Fast algorithm for electromagnetic scattering by buried 3-D dielectric objects of large size

A fast algorithm for electromagnetic scattering by buried three dimensional (3-D) dielectric objects of large size is presented by using the conjugate gradient (CG) method and fast Fourier transform (FFT). In this algorithm, the Galerkin method is utilized to discretize the electric field integral equations, where rooftop functions are chosen as both basis and testing functions. Different from the 3-D objects in homogeneous space, the resulting matrix equation for the buried objects contains both cyclic convolution and correlation terms, either of which can be solved rapidly by the CG-FFT method. The near-scattered field on the observation plane in the upper space has been expressed by two-dimensional (2-D) discrete Fourier transforms (DFTs), which also can be rapidly computed. Because of the use of FFTs to handle the Toeplitz matrix, the Sommerfeld integrals´ evaluation which is time consuming yet essential for the buried object problem, has been reduced to a minimum. The memory required in this algorithm is of order N (the number of unknowns), and the computational complexity is of order N_iterN log N, in which N_iter is the iteration number, and N_iter≪N is usually true for a large problem