Abstract
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.
Highlights
Analysis of metal structures placed in a planar multilayered environment has been of interest to the community of researchers dealing with computational electromagnetics for decades
In free-space problems, limitations due to the computational complexity of order O(N3), when applying direct methods like LU decomposition, are usually overcome by using Krylov-subspace iterative methods with techniques like fast multipole method (FMM) [2] or low rank integral equations (IE)-QR algorithm [3] applied to speed-up computation of matrix-vector product
This may be attributed to the fact that for far-lying patches the coupling mechanism is dominated by surface waves phenomena, so extracting the FMM part does not reduce r in the incomplete QR (iQR), while adding unnecessary overhead into the computation time
Summary
Analysis of metal structures placed in a planar multilayered environment has been of interest to the community of researchers dealing with computational electromagnetics for decades. In free-space problems, limitations due to the computational complexity of order O(N3), when applying direct methods like LU decomposition, are usually overcome by using Krylov-subspace iterative methods with techniques like fast multipole method (FMM) [2] or low rank IE-QR algorithm [3] applied to speed-up computation of matrix-vector product. Both techniques allow for reducing the cost of a single iteration from O(N2) to O(N3/2) in the case of the single-level method, or to O(N log N ) in the case of its multilevel counterpart, in the case of FMM called multilevel fast multipole algorithm (MFLMA) (cf [2, 3]).
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