On the Application of the Incomplete QR Algorithm to the Analysis of Microstrip Antennas

Abstract

In this paper, we provide some insight into the usage of fast, iterative, method-of-moments (MoM) solution of integral equations (IE) describing antennas and other metallic structures immersed in a planar multilayered environment. Based on the form of multilayered media Green's functions, we extract free-space terms, associated with direct rays within the analyzed structure, reducing the number of significant interactions required to describe the rest of MoM matrix. Next, we show that it is possible to construct a hybrid algorithm, where the fast multipole method (FMM) is used to the free-space matrix part, while the reduced rank incomplete QR (iQR) decomposition is applied to the remaining portion of the MoM matrix. This HM-iQR (hybrid multipole - incomplete QR) method is applied to a relatively large (in terms o f the number of unknowns) problem of plane wave scattering by a finite array of rectangular microstrip patches printed on a grounded dielectric slab. Computation results from the new algorithm are compared to literature data and to the results of the pure low rank IE-QR method.