i
ABSTRACT
In this thesis, the Method of Moments (MoM) is deeply described and used for the analysis of electromagnetic (EM) radiation and scattering problems involving arbitrarily shaped 3D targets. The proposed MoM formulation allows us to investigate perfect and imperfect conductor and dielectric object. Next, a novel method for efficient MoM analysis of electrically large objects using Characteristic Basis Functions (CBFs) is proposed to reduce the matrix solution time. The CBFs are special types of high-level basis functions, defined over the domains that encompass a relatively large number of conventional sub-domain bases, e.g., triangular patches or rooftops. The original geometry is divided into N blocks, and the primary and secondary CBFs are constructed for each block. The primary CBF for a particular block is associated with the solution for the isolated block, while the secondary ones account for the mutual coupling effects between itself and the remaining blocks. This technique differs from other similar approaches previously developed, in several aspects. First of all, it includes mutual coupling effects directly by using primary and secondary CBFs, which are then used to represent the unknown induced currents on the blocks, and solved via the Galerkin method rather than using iterative refinements. Additionally, the Characteristic Basis Function Method (CBFM) is more general, and can be applied to a wide class of electromagnetic problems.
ii Finally, we present new approaches to speed up the analysis of scattering problems by using the CBF methodology previously described. Moreover, a frequency independent version of the CBFM is introduced. The basic idea is to use Singular Value Decomposition (SVD) to obtain a set of frequency-independent CBFs. This new type of high level basis functions are computed at higher frequencies: from the knowledge of the solution at higher frequencies, we obtain the solution at lower frequency with a huge save in computational time. We demonstrate the potential and applicability of the proposed methods by applying them to generic three-dimensional scattering problems.
