This paper presents an analysis of electrically large antennas using the adaptive integral method (AIM). The arbitrarily shaped perfectly conducting surfaces are modeled using triangular patches and the associated electric field integral equation (EFIE) is solved for computing the radiation patterns of these antennas. The method of moments (MoM) is used to discretize the integral equations and the resultant matrix system will be solved by an iterative solver. The AIM is employed in the iterative solver to speed up the matrix-vector multiplication and to reduce the memory requirement. As specific applications, radiation patterns of parabolic reflectors and X-band horns are computed using the proposed method.

We describe elements of a fast integral equation solver for large periodic and partly periodic finite array systems. A key element of the algorithm is utilization (in a rigorous way) of a block-Toeplitz structure of the impedance matrix in conjunction with either conventional Method of Moments (MoM), Fast Multipole Method (FMM), or Fast Fourier Transform (FFT)-based Adaptive Integral Method (AIM) compression techniques. We refer to the resulting algorithms as the (block-)Toeplitz-MoM, (block-)Toeplitz-AIM, or (block-)Toeplitz-FMM algorithms. While the computational complexity of the Toeplitz-AIM and Toeplitz-FMM algorithms is comparable to that of their non-Toeplitz counterparts, they offer a very significant (about two orders of magnitude for problems of the order of five million unknowns) storage reduction. In particular, our comparisons demonstrate, that the Toeplitz-AIM algorithm offers significant advantages in problems of practical interest involving arrays with complex antenna elements. This result follows from the more favorable scaling of the Toeplitz-AIM algorithm for arrays characterized by large number of unknowns in a single array element and applicability of the AIM algorithm to problems requiring strongly sub-wavelength resolution.

In this paper, we present the interlaced fast Fourier transform (FFT) method to parallelize the adaptive integral method (AIM) algorithm for the radar cross-section (RCS) computation of large scattering objects in free space. It is noted that the function obtained after convolution is smoother as compared to the original functions. Utilizing this concept, it is possible to interlace the grid current and charge sources in AIM and compute the potentials on each set of interlaced grid independently using FFT. Since the potentials on each interlaced grid are smooth functions in space, we can then interpolate the potentials to every other nodes on the original grid. The final solution of the potentials on the original grid is obtained by summing the total contributions of all the computed and interpolated potentials from every individual interlaced grid. Since the potentials of each interlaced grid can be computed independently without much communication overheads between the processes, such an algorithm is suitable for parallelizing the AIM solver to run on distributed parallel computer clusters. It is shown that the overall computation complexity of the newly proposed interlaced FFT scheme is still of O(N log N).