A fast analysis of scattering from large-scale finite periodic microstrip patch arrays arranged on a non-orthogonal lattice using sub-entire domain basis functions

A sub-entire domain (SED) basis function method, which was first introduced for modeling large-scale finite periodic PEC structures in free space, has been extended for fast characterization of electromagnetic scattering from an electrically large planar finite periodic microstrip patch array. The microstrip array may have a nonrectangular layout and non-orthogonal lattice configurations (e.g., hexagons or quadrangles). Based on the mixed potential integral equation, and utilizing the proposed SED basis function algorithm, the original large-scale finite periodic array of microstrip patches can be efficiently simulated by decomposing it into two problems with matrix equations of small dimensions. The first is to construct the SED basis functions for the corresponding microstrip arrays with orthogonal/non-orthogonal lattices. Three kinds of the SED basis functions are constructed, including those related to the edge patch elements, the interior patch elements, and the corner patch elements. The second is to solve the system equation with significantly reduced problem dimension as compared to the original larger problem. Based on the obtained SED basis functions, the reduced matrix equation of small size can be generated by the Galerkin procedure, and solved by use of the LU (lower-upper) decomposition-based direct solver, which results in a fast solution. The accuracy and efficiency of the developed algorithms are demonstrated by numerical tests that include the scattering from several large-scale finite periodic arrays of microstrip patches with rectangular, non-orthogonal lattices.