The multilevel Green's function interpolation method and its application in the analysis of microstrip antenna array

Abstract

This research work is on the improvement of the multilevel Green's function interpolation method (MLGFIM) and its application in the analysis of electrically large multilayered problems, e.g., the microstrip antenna array. The microstrip antenna and its array have been used in many applications because they are easy and inexpensive to fabricate. Many algorithms can be used to analyze the microstrip antennas, including the method of moment (MoM), the finite element method (FEM), the finite differential time domain method (FDTD), etc. To analyze the microstrip structure, the problem domain is usually modeled and discretized. Then the integral equation or differential equation associated with the problem is transformed into a matrix equation, which is then solved by an iteration method. When MoM is applied to analyze the microstrip antenna, only the antenna element and feeding network are discretized, the effect of the substrate and ground plane can be taken into account by the Green's function associated with the multilayered medium, i.e., the multilayered Green's function. So the number of unknowns is much reduced compared with other algorithms, which makes MoM more suitable for the simulation of electrically large microstrip structures. When MoM is applied to solve the multilayered problem, the first step is to calculate the multilayered Green's function, which is constituted of a dyadic Green's function and a scalar Green's function. Each component of the Green's function involves the evaluation of an integral named the Sommerfeld integral (SI). Generally the analytical solution of SI is not available and the direct numerical integration is very time-consuming. Many fast algorithms have been proposed to evaluate this integral. The discrete complex image method (DCIM) is one of these algorithms, which is efficient and easy to implement, but one problem of this method is that the numerical accuracy is not quite stable in the far-field calculation. In this research work, a special sampling path is proposed to improve the numerical stability of the algorithm in the far-field region. The direct application of MoM will generate a dense matrix equation. When this equation is solved by the iteration method, a large number of matrix-vector multiplications (MVMs) are required. The computational complexity for one multiplication is O(N2), which is prohibitively high for practical applications. In this research work, the MLGFIM will be applied to reduce the complexity from O(N2) to O(NlogN). In the implementation of the MLGFIM, a hybrid 2D and 3D (H2D/3D) multilevel partitioning technique is devised for the specific problem. The interpolation of the multilayered Green's functions is studied for the first time, which shows that the interpolation technique is still valid and efficient for the multilayered problem, although the interpolation has to be performed on different Green's function components. The fast Fourier transform (FFT) is also incorporated into the MLGFIM to accelerate the translation procedure, which reduces the complexity of the algorithm further. With this H2D/3D MLGFIM-FFT algorithm, the computation of the MVM is much accelerated. Another benefit obtained from the fast algorithm is that the parallel computation is straightforward. The fast algorithm (viz. the H2D/3D MLGFIM-FFT) only speeds up the computation of the MVM, which is not enough to solve the electrically large multilayered problem. When the electrical size of the antenna array is very large, the convergence of the iteration process will be a big problem. The complicated wave nature associated with the multilayered medium will make the problem more serious. Preconditioning techniques are indispensable for solving this kind of problem, which helps to improve the condition number of the impedance matrix. In this work, the block version of the sparse approximation inverse (SAI) preconditioning technique is incorporated into the fast algorithm. With this preconditioner, the microstrip antenna array with over 1,000 elements is successfully solved in reasonable time. Besides the typical microstirp antenna, the antennas integrated with matematerials, e.g. the electromagnetic band-gap (EBG) structure and metasurface, are also analyzed with the proposed algorithm.

Date of Award	16 Feb 2015
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Chi Hou CHAN (Supervisor)