Fast Full-Wave Methods for Aperiodic Antenna Arrays for Space Applications

This dissertation presents the Higher-Order Array Decomposition Method (HO-ADM), a fast, accurate yet versatile full-wave analysis technique applicable for electrically large arrays of antennas or scatterers, as they are typical for space applications, including sparse, connected, and non-identical-element arrays. The HO-ADM exploits the multi-level block-Toeplitz (MBT) property of the Method of Moments (MoM) matrix in case of regular arrays, permitting an FFT-accelerated matrix-vector product (MVP) to achieve asymptotic computational and memory complexities of O(N logN) and O(N), respectively, where N is the number of unknowns.

The combination of ADM with higher-order (HO) hierarchical Legendre basis functions (BFs) generally yields an order of magnitude reduction in both computation time and memory consumption as compared to using first-order BFs. For example, a 40 times reduction in total computation time and a ten times reduction in memory consumption is achieved for a 100-element Direct Radiating Array (DRA) of conical
horns on a laptop, resulting in a computation time of five minutes compared to over three hours with first-order BFs.

Several extensions of the HO-ADM are presented including capabilities for analyzing sparse array antennas, arrays with electric conduction currents between elements, arrays with non-identical elements, and arrays with dielectric substrates. The analysis of sparse array antennas is achieved by using a technique to implicitly keep the MoM matrix for a fully populated array, thus preserving the FFT-accelerated MVP, and by employing a constrained Krylov subspace in the iterative solver. The extension to arrays with electric conduction currents between elements is accomplished by introducing half-doublet BFs at connected boundaries, using the Discontinuous Galerkin Method (DGM) to enforce current continuity, and by introducing auxiliary unknowns to retain the MBT property of the MoM matrix. The analysis of arrays with non-identical elements is realized by introducing the concept of a Super Unit Cell (SUC) from which individual mesh-regions can be excluded from the iterative solution process.

Finally, the analysis of connected and simultaneously closed structures, including dielectric substrates, is made possible by introducing a method of internal walls and internal equivalent currents, and by employing the Poggio-Miller-Chang-Harrington- Wu-Tsai (PMCHWT) integral equation formulation.

Numerous numerical tests have confirmed the efficacy and accuracy of the presented extensions, from which it is evident that the HO-ADM, generally, is more than an order of magnitude faster than a state-of-the-art Higher-Order Multi-level Fast Multipole Method (HO-MLFMM) implementation. This performance is achieved with a memory consumption of HO-ADM which is reduced or comparable to HOMLFMM. For example, a 32 × 32 = 1024-element connected all-metal antenna array designed for the Europa Lander mission is analyzed on a laptop within six minutes with one million unknowns with HO-ADM, compared to approximately one hour for HO-MLFMM. Another example is a 8 × 128 = 1024-element patch array with nonidentical elements which is solved with HO-ADM in three minutes compared to half an hour for HO-MLFMM. Additionally, results demonstrate efficient and accurate analysis of a 20 × 20 = 400-element array of PEC cylinders embedded in a dielectric substrate. Moreover, a finite thickness PEC plate with 2500 holes, analyzed as a 50 × 50-element array of identical elements with the HO-ADM is solved with a total computation time of four minutes, compared to 68 minutes with HO-MLFMM.

The developed method represents a significant advancement in the field of computational electromagnetics applied to the simulation of electrically large arrays of antennas or scatterers. Through a rigorous application of an FFT-accelerated MVP, the computation times compared to an existing fast method based on the MLFMM are reduced by at least a factor of ten, while at the same time maintaining a comparable
memory consumption or even less. The tremendous acceleration in computation speed makes the design and optimization of state-of-the-art antenna arrays more efficient and reduces significantly the time to market.