The Ewald method is applied to accelerate the evaluation of the Green’s function of an infinite periodic phased linear array of point sources. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy.

A straightforward numerical analysis of large arrays of arbitrary contour (and possibly missing elements) requires large memory storage and long computation times. Several techniques are currently under development to reduce this cost. One such technique is the GIFFT (Green's function interpolation and FFT) method discussed here that belongs to the class of fast solvers for large structures. This method uses a modification of the standard AIM approach [1] that takes into account the reusability properties of matrices that arise from identical array elements. If the array consists of planar conducting bodies, the array elements are meshed using standard subdomain basis functions, such as the RWG basis. The Green's function is then projected onto a sparse regular grid of separable interpolating polynomials. This grid can then be used in a 2D or 3D FFT to accelerate the matrix-vector product used in an iterative solver [2]. The method has been proven to greatly reduce solve time by speeding up the matrix-vector product computation. The GIFFT approach also reduces fill time and memory requirements, since only the near element interactions need to be calculated exactly. The present work extends GIFFT to layered material Green's functions and multiregion interactions via slots in ground planes. In addition, a preconditioner is implemented to greatly reduce the number of iterations required for a solution. The general scheme of the GIFFT method is reported in [2]; this contribution is limited to presenting new results for array antennas made of slot-excited patches and cavity-backed patch antennas. © 2005 IEEE.

Diffraction effects on truncated periodic structures at the field operator level are examined. A physically-based approximate operator inverse of the electric field integral equation (EFIE) is used to either obtain an accurate first estimate of element currents, or as a preconditioner for a more rigorous, iterative solution. For illustration purposes, linear arrays of cylindrical elements are analyzed. The reduction in the matrix solution time that is achieved is shown. Furthermore, the physical insight into array truncation effects that the method provides is discussed.

An alternative direct procedure for applying the Ewald approach to obtain the Green's function for an array of line sources with 1D periodicity is presented. Furthermore, an algorithm for choosing the Ewald splitting parameter E that extends the efficiency of the method when the periodicity is somewhat larger than a wavelength is derived. In particular, the dyadic Green's function formalism is combined with the Ewald method.

A new type of fest method of moments (MoM) solution scheme using standard basis functions for large arrays with arbitrary contours and/or missing elements is applied to array antennas in a layered configuration. The efficiency of the method relies on use of the FFT along with approximating the Green's function as a separable sum of interpolation functions defined on a relatively sparse, uniform grid. The method is ideally suited for solving array problems, and its effectiveness is demonstrated here for planar arrays of printed antennas. Both fill and solve times, as well as memory requirements, are dramatically improved with respect to standard MoM solvers. © 2006 ACES.

The Ewald method is applied to accelerate the evaluation of the Green's function (GF) of an infinite equispaced linear array of point sources with linear phasing. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. It is shown analytically that the choice of the standard "optimal" Ewald splitting parameter E0 causes overflow errors at high frequencies (period large compared to the wavelength), and convergence rates are analyzed. A recipe for selecting the Ewald splitting parameter is provided. © 2006 Elsevier Inc. All rights reserved.

An efficient semianalytical algorithm for the evaluation of the field and modal excitation by a line source in a two-dimensional electromagnetic bandgap (EBG) waveguide is presented. The method allows for an accurate and efficient calculation of the near field from the source inside the EBG waveguide, as well as the amplitude of the EBG waveguide mode that is excited. The same method can be applied to a wide variety of structures, as well as other types of sources and discontinuities.

A new type of fast method of moments (MoM) solution scheme for large arrays is developed using standard basis functions. Both fill and solve times are improved with respect to standard MoM solvers. The efficiency of the method relies on approximating the Green's function as a sum of separable interpolation functions defined on a relatively sparse uniform grid, along with use of the fast Fourier transform. The method permits the analysis of arrays with arbitrary contours and/or missing elements. Preliminary results show the effectiveness of the method for planar array elements in free space.