Recursive T-Matrix Algorithms for the Solution of Electromagnetic Scattering from Strip and Patch Geometries

Two recursive T-matrix algorithms (RTMA’s) are presented and their reduced computational complexities and reduced memory requirements are demonstrated. These algorithms are applied to the problem of electromagnetic scattering from conducting strip and patch geometries. For a systematic development, canonical geometries of strips and patches are chosen. These geometries are reminiscent of finite-sized frequency selective surfaces (FSS’s). Computational complexities of O(N2) and O(N7/3) and memory requirements of O(N) and O(N4/3) are shown to be feasible for two-dimensional and three-dimensional geometries, respectively. The formulation uses only two components of the electric field. Therefore, the vector electromagnetic problem of scattering from three-dimensional patch geometries can be solved using scalar—rather than vector—addition theorems for spherical harmonic wave functions. For a two-dimensional strip problem, both TM and TE polarizations can be solved simultaneously using this formulation. Numerical scattering results are presented in the form of radar cross sections (RCS’s) and validated by comparison with the method of moments (MoM).