CONCLUSION
The purpose of this thesis has been to develop numerically efficient techniques to alleviate the problems encountered when the Method of Moments (MoM) is applied to electrically large electromagnetic scattering problems. As the analyzed object becomes large in terms of wavelength, the MoM gets highly inefficient due to the long computer running time and huge primary memory it requires. In order to circumvent these problems, we have introduced two methods: the Characteristic Basis Functions Method (CBFM) and the Extrapolation Technique.
In this work, we have shown that direct or iterative solvers are not the most efficient ways to solve the dense, large, and linear systems arising from the application of the Method of Moments. In fact, the proposed CBFM has been more efficient, in terms of reduction of the memory requirement and execution time, than the previously mentioned solvers. It has also been demonstrated that the CBFM is a powerful and general method, which differs from other similar approach in several aspects. First, it includes the mutual coupling rigorously. Second, it leads to a small-size matrix that can be solved directly giving an inverse matrix, which is independent on the excitation.
Third, it is a general method because it can be applied to a wide class of EM problems.
We have demonstrated the accuracy and the powerfulness of the CBF method by several examples and through comparison of its solutions with direct ones. All these
101
comparisons have shown excellent agreements and have served to validate the CBF method. Moreover, it has been proved the reduction in the storing requirement and computational effort. Most important, it has been demonstrated that the CBFM can solve electrically very large problems that are unsolvable by using conventional MoM codes.
Also, a novel method, based on an extrapolation technique, has been developed to contrast the long execution time encountered in a frequency analysis of a large body using the MoM. This approach, which is limited to scattering problems, has been shown to be an efficient technique for reducing the computational effort involved in such problems. It has been applied to an infinite and electrically large cylinder.
Numerical results obtained for this 2-D scattering problem have demonstrated the validity and effectiveness of the idea. In fact, we have predicted the solution at high frequency with a relatively small error and have realized an enormous saving in the computational time. We anticipate that this method can be generalized to apply to any scattering problems involving arbitrarily shaped objects.
