| Application of the method of moments (MoM) for analyzing large and complex structures is limited by its O(N 2) memory requirements and solution time, where N is the number of unknowns. In this thesis, an efficient adaptive algorithm is presented for fast simulation of large scale electromagnetic problems in low frequency applications.;The approach is based on an approximation of the Green's function by a series of evanescent and propagating plane waves, and an adaptive multi-level grouping of the sources. The most important advantage of the proposed method is its stability at low frequencies. This is due to the use of evanescent waves in the expansion, which gives a very accurate representation of the field for distances very close to the source. The proposed algorithm reduces the complexity of the matrix-vector multiplication from O( N2) to less than O(N log N). It is combined with an iterative method to efficiently solve the MoM matrix equation in low frequency applications.;In addition, a novel and very fast method for evaluating the space domain Green's function of general multi-layer media is presented in this thesis. The approach is based on the plane wave expansion of the source incident field, and the reflection and transmission of plane waves at the boundaries of the layered medium. The same set of plane waves can be used to obtain the Green's function for media with different parameter values, over a wide range of frequencies. Also, the same set of plane waves are used to evaluate various vector and scalar potential Green's functions. The important feature of this representation is that the spatial domain Green's function is expanded in terms of simple exponential functions. This makes it possible to incorporate the proposed representation in a fast plane wave expansion algorithm to accelerate the MoM solution of multi-layered structures, at low frequency applications. This includes analysis and design of highly integrated circuits and miniature low profile antennas and arrays, with dimensions small or comparable to the wavelength, but containing very small and important features. |
