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Conclusion
In this thesis a numerically efficient technique to analyze electrically large problem has been presented. As discuss in this work, the method of moments loses efficiency when the dimension of the analyzed object is some wavelength, because the most intensive task in the method is the inversion of the impendence matrix, which dimension is related at the number of unknowns. It follows that can be impossible solve large problem without the suitable computing capacity. In the literature several methods are proposed to solve this problem, both with direct solution that iterative.
A method that offers several advantages is definitely the Characteristic Basis Function Method.
The peculiarity of this method is the ability to decompose a large problem into smaller problems and therefore more easily solved. Electrically, very large problems can be handled since CBFM allows a decrease in the matrix size compared to that obtained by RWG. This matrix, also known as reduced matrix, is sparse and well-conditioned in nature, and it can be addressed through direct solvers rather than iterative methods. In addition, through the use of the plane wave spectrum technique, the CBFs provide a complete knowledge of the electromagnetic behavior of the object. If we were interested in knowledge about the radar cross section of scattering in general or of a metal object, we can change the excitation, therefore the incident plane wave, without having to recalculate the CBFs themselves. Hence, CBFM does not suffer convergence problems and can solve multiple excitation problems efficiently. The CBFM is a highly parallelizable method, each blocks can be analyzed by a processor, resulting in an excellent saving of time and a better management of the computing resources.
The proposed technique of re-use of the Characteristic Basis Functions (CBFs) calculated at the highest frequency of the band, termed Ultra-wide band Characteristic Basis Functions (UCBFs), leads to a significant reduction of solver time with respect to conventional CBFs procedure, and this is achieved by always maintaining all the advantages of CBFM. We demonstrated the accuracy and the effectiveness on the proposed scheme via several numerical examples. Finally, using UCBFs guarantees that the condition number of the reduced matrix does not grows significantly when moving to lower frequencies.
Furthermore, an extension of the CBFM for handling scattering problems involving structures with apertures (slots) has been presented. It has been demonstrated that the problem can be solved by filling the slots with PEC and applying the CBFM to the entire structure, using an
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appropriate magnetic current densities, which are calculated separately by solving local problems. Several numerical examples have been presented to validate the procedure and the results have been compared with those obtained through a commercial software, when possible. Moreover, concerning the radiation by aperture antenna, Mode Matching (MM)/Finite Element Method (FEM) can be used to evaluate the local problem, and spectral rotation can be employed to efficiently calculate the coupling between apertures. It is important to highlight that it possible to separate the local problem, i.e. calculate of magnetic current and relative radiated electric field of an aperture antenna, from the global problem, i.e.
solving the problem of an slot antenna array mounted on a PEC tridimensional object.
