On matrix partitioning, the Sherman-Morrison-Woodbury technique and the add-on method

The moment method matrix is compared with the add-on technique for the analysis of scattering from large planar structures. It is shown that the two formulations yield the same results, provided that the physical model, the basis and testing functions, and the truncation and discretization criteria are the same. The differences lie in the numerical routes taken to arrive at those results. The numerical advantages of the add-on technique are clearly shown. Consideration is also given to the Sherman-Morrison-Woodbury technique, which has been used for adapting existing moment method codes, within their limitations, to account for changes in the configuration. It is noted, however, for the case where the changes are additions of segments to the original structure, as in the present case, that this scheme coincides with the matrix partitioning scheme discussed here and that it provides no further advantage.<>