Numerical, asymptotic and hybrid methods for large array analysis

A relatively fast and efficient preconditioned iterative method of moments solution is developed for solving an integral equation governing the array element currents on large, planar, periodic arrays of printed elements/slots in a grounded multilayered medium. This solution is highly suitable for calculations on a personal computer (PC). The large finite arrays are assumed to be embedded in a grounded multilayered medium of infinite extent. Hence, a Green´s function for the latter geometry is utilized as the kernel of the governing array integral equation to restrict the number of unknowns to be solved to only the element currents; this Green´s function is evaluated asymptotically in closed form for source and observation points which are separated laterally over a distance of one free space wavelength or larger. The latter provides an additional, significant speed up of this solution. Also, a ray method is developed to rapidly evaluate the fields radiated/scattered by the array currents found via the above numerical method of moments solution of the corresponding array radiation/transmitting or scattering/receiving problem. These ray fields describe the collective radiation / scattering from the whole array at once, and provide a physical picture for the array radiation /scattering. Next, a hybrid combination of ray and method of moments is developed to drastically reduce the number of unknowns to be solved as compared to the conventional method of moments. The moment method matrix equation can be treated by a direct solver in this hybrid approach because of the presence of the relatively very few unknowns (of the order of hundred) irrespective of the array size. This is in contrast to the iterative solver for the array currents based on the preconditioned moment method approach mentioned in the beginning, which solves for the conventional number of unknowns (that are greater than or equal to the number of array elements; e.g. the number of unknowns in the itera- tive approach is of the order of hundreds of thousands for an array of tens of thousands of elements, as compared to only in the hundreds for the hybrid direct solver approach). Finally, the ideas which are developed and utilized in the hybrid ray-numerical approach for large planar arrays are significantly modified and extended to potentially treat realistic doubly curved large finite conformal arrays of complex elements embedded in multilayered media, including a radome that is flush with the skin line of an even larger metallic platform (such as an aircraft) in which the array is placed. Numerical results will be presented to illustrate the accuracy of all the above approaches.