Analysis of Large Complex Structures with the Synthetic-Functions Approach

An innovative procedure is presented that allows the method of moments (MoM) analysis of large and complex antenna and scattering problems at a reduced memory and CPU cost, bounded within the resources provided by a standard (32 bit) personal computer. The method is based on the separation of the overall geometry into smaller portions, called blocks, and on the degrees of freedom of the field. The blocks need not be electrically unconnected. On each block, basis functions are generated with support on the entire block, that are subsequently used as basis functions for the analysis of the complete structure. Only a small number of these functions is required to obtain an accurate solution; therefore, the overall number of unknowns is drastically reduced with consequent impact on storage and solution time. These entire-domain basis functions are called synthetic functions; they are generated from the solution of the electromagnetic problem for the block in isolation, under excitation by suitably defined sources. The synthetic functions are obtained from the responses to all sources via a procedure based on the singular-value decomposition. Because of the strong reduction of the global number of unknowns, one can store the MoM matrix and afford a direct solution. The method is kernel-free, and can be implemented on existing MoM codes.