Multi-level decomposition approach to translational symmetry problems of several dimensions

Summary form only given. Finite antenna arrays consisting of regularly-spaced, arbitrarily-shaped and identical elements exhibit translational symmetry. This property can easily be exploited in conventional planar (2D) arrays, and the concept can also be applied to structures of higher dimensionality. The rigorous analysis of complex antenna elements in a finite array has been successfully carried out using the finite element-boundary integral (FE-BI) method along with a decomposition approach. In these techniques, complicated and distributed systems are modelled by decomposing the structures into like blocks, where possible, for storage and computational savings. This approach is quite efficient in most regards and when applied to finite array problems, we refer to it as the array decomposition method (ADM). It is quite successful for smaller arrays, but results in a linear increase of matrix storage for increasingly large array problems. To counter the storage problem, the approach was extended to include far-zone decomposition via the fast multipole method (FMM) (Kindt, R. and Volakis, J.L., Radio Science, 2003). This newer approach limits the near-zone interaction storage of array systems to a small number of terms. This combination of simultaneous near-zone and far-zone decompositions, the array decomposition-fast multipole method (AD-FMM), results in fixed near-zone matrix storage, and overall storage requirements of O(N) for any sized array with a system with a total of N degrees of freedom. The effectiveness of this approach for several interesting problem types is discussed.