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In this paper, we provide some insight into the us- age of fast, iterative, method-of-moments (MoM) solution of integral equations (IE) describing antennas and other metal- lic structures immersed in a planar multilayered environ- ment. 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 thefree-spacematrixpart,whilethereducedrankincomplete 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 un- knowns) problem of plane wave scattering by a finite array of rectangular microstrip patches printed on a grounded di- electric slab. Computation results from the new algorithm are compared to literature data and to the results of the pure low rank IE-QR method.

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