A novel and effective iterative scheme of the progressive numerical method (PNM) combined with MoM is well applied to a fast analysis of a large waveguide slot antenna array in this paper. The iterative process of overlapping slot regions takes into account the internal and external coupling of slots effectively. Since the external mutual coupling decreases with distance, the overlapping slot regions can be smaller, which speeds up the MoM analysis of slot antenna array greatly. Some numerical results are given to illustrate the high efficiency and accuracy of the proposed approach.

A Progressive Numerical Method Combined with MoM for a Fast Analysis of Large Waveguide Slot Antenna Array

Techniques for solving electromagnetic scattering from electrically large structures are studied. Two techniques, the progressive numerical method (PNM) and the spatial decomposition technique (SDT), are applied to study the two-dimensional problems of perfectly conducting objects with TM and TE plane wave illuminations. Both PNM and SDT are based on the method of moments (MoM) and divide the objects into a number of small regions and hence reduce the matrix size and computer time. The PNM uses the concept of overlapping regions. Accurate solutions can be obtained for the TM case and good agreement with the full matrix MoM can be achieved for the TE case. It is found that the SDT needs modification, by not taking into account the virtual interface currents between the two adjacent regions and the iteration procedure is only useful for the TM case. It is also shown that, the modified SDT is a special case of PNM in which there is no overlapping region. Finally, it is found that the PNM is an efficient way to eliminate the internal resonances of scattering problems.

Performance of the progressive numerical method and its comparison with the modified spatial decomposition technique in solving large scattering problems

The progressive numerical method (PNM) is an effective way of dealing with electromagnetic scattering by electrically large objects. The PNM is based on the moment methods (MM). It is known that the solutions of the electric or magnetic field integral equations, using the MM, can be reduced to a matrix equation. The process of the PNM is started by selecting a small region at the centre of the illuminated side of the scatterer to reduce the interactions from the remaining sections of the object. However it is usually difficult to do so for asymmetrical scatterers. It is also noted that the accuracy of the solutions for the TE case is poorer than that of the TM case. This is due to the fact that for the TE case the induced currents are circumferential. An iterative step is incorporated with the PNM for better accuracy. To examine the behavior of the solution using iterative PNM, a perfect conducting infinite rectangular cylinder (TM case) is assumed.

Large electromagnetic scattering computation using iterative progressive numerical method

This paper presents various types of iterative progressive numerical methods (IPNMs) for the computation of electromagnetic (EM) wave scattering from many objects and reports comparatively the performance of these methods. The original IPNM is similar to the Jacobi method which is one of the classical linear iterative solvers. Then the modified IPNMs are based on other classical solvers like the Gauss-Seidel (GS), the relaxed Jacobi, the successive overrelaxation (SOR), and the symmetric SOR (SSOR) methods. In the original and modified IPNMs, we repeatedly solve linear systems of equations by using a nonstationary iterative solver. An initial guess and a stopping criterion are discussed in order to realize a fast computation. We treat EM wave scattering from 27 perfectly electric conducting (PEC) spheres and evaluate the performance of the IPNMs. However, the SOR- and SSOR-type IPNMs are not subject to the above numerical test in this paper because an optimal relaxation parameter is not possible to determine in advance. The evaluation reveals that the IPNMs converge much faster than a standard BEM computation. The relaxed Jacobi-type IPNM is better than the other types in terms of the net computation time and the application range for the distance between objects.

A Comparative Study on Iterative Progressive Numerical Methods for Boundary Element Analysis of Electromagnetic Multiple Scattering

Unlike quasi-optical techniques such as the Geometrical Theory of Diffraction (GTD), the Method of Moment (MoM) provides accurate and essential surface current information. For the electromagnetic scattering analysis of electrically large, perfectly electric conductor (PEC) bodies, several fast and efficient “Decompose-Solve-Recompose” (DSR) schemes are available in the literature. Among these, the Progressive Numerical Method (PNM) is a scatterer sectioning method that accounts for the progressive effect of previously computed surface current solutions [1]. In these scatterer decomposition techniques, coupling effects from adjacent subregions are included into the computation of each subregion. Typically, such techniques are especially suitable for very large scatterers since their solution accuracies improve with larger body sizes and are insensitive to their subregion sizes [2].

A PNM implementation for large phased arrays

It is shown that the numerical solution of electromagnetic scattering problems using moment methods can be carried out in a progressive manner by dividing the scattering surface into several small regions. The technique reduces the large matrix of the conventional moment method into several small matrices on the regions and enables one to solve easily the problem of scattering by very large objects. The accuracy of the method and the criteria for controlling computational errors are examined by its application to two-dimensional problems. Both parallel and perpendicular polarizations are assumed and the behaviour of the solutions for both smooth and singular field distributions on circular cylinders and prisms is studied. It is found that the surface distributions, such as induced currents, may be obtained more accurately by this method than the conventional moment method. The accuracy of the far fields, however, are generally of the same order for both methods. For convenience and brevity, the term PNM is used to refer to the method throughout this paper.

L. Shafai

Papers

A progressive numerical method and its application to large field problems in antennas and electromagnetic scattering