A Fast IE-FFT Algorithm to Analyze Electrically Large Planar Microstrip Antenna Arrays

A fast integral-equation fast Fourier transform (IE-FFT) algorithm is developed, analyzed, and applied to the electromagnetic solution of radiation problems. The solution begins by the method-of-moments solution of a mixed potential integral equation on electrically large antenna arrays. Similar to other grid-based algorithms, the IE-FFT uses a Cartesian grid to significantly reduce memory requirement and speed up CPU time for both matrix assembly and matrix-vector multiplication when used with an iterative solver. The IE-FFT algorithm employs two discretizations, one for unknown current on an unstructured triangular mesh and the other on a uniform Cartesian grid for interpolating the layered medium's Green's functions. The uniform interpolation of the Green's functions allows us a global FFT for well-separated far-interaction terms. However, the near-interaction terms should be effectively corrected. A simple and efficient Lagrangian interpolation of the Green's functions is proposed. For a 2.5-D planar layered structure problem, the complexity of an IE-FFT is found to approximately <inline-formula> <tex-math notation="LaTeX">$O(N)$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX"> $O({N\,{\rm{log}}\,N})$</tex-math></inline-formula> for memory and CPU time, respectively.