| In this thesis, wavelet applications for a fast solution of electromagnetic integral equations are thoroughly studied. Wavelet bases offer the advantage of highly sparse moment-method matrix equations, which can be solved efficiently. The performance of semi-orthogonal and orthogonal wavelets when used for a fast solution of Fredholm integral, equations, which arise in the formulation of wave scattering by two-dimensional conducting cylinders, is first investigated. This basic research consists in the analysis of matrix sparsity, solution accuracy, and matrix condition number, and provides a guideline for the selection of wavelets used for the fast solution of electromagnetic integral equations. It was discovered that the orthogonal wavelets are optimal in terms of the condition number. Then, two kinds of wavelet applications to the method of moments, i.e., the matrix transform approach and the change-of-bases scheme, are compared for the first time for the solution of coupled scalar integral equations governing the problem of scattering by two-dimensional dielectric bodies. The study shows that the change-of-bases scheme gives rise to a better performance in terms of matrix sparsity, while the matrix transform approach provides a problem-independent transform mechanism. Further, the matrix transform approach with orthogonal wavelets is extended to a fast analysis of the scattering by arbitrary bodies of revolution, whose mathematical model contains coupled vector integro-differential equations. Finally, the application of wavelets is effectively used for a fast solution of scattering problems by 3-D inhomogeneous bodies of arbitrary shape, which is formulated as a volume integral equation involving equivalent sources.; Several solution methods for the resultant sparse matrix equations, obtained with the use of wavelets, are also investigated. The conjugate or bi-conjugate gradient (BiCG) iterative algorithms are popular solvers used in the computational electromagnetics community. A sparse conjugate gradient algorithm is effectively used for a fast solution of Fredholm integral equations. A sparse BiCG, with an efficient wavelet transform technique for Toeplitz matrices, is also presented for the fast solution of 3-D volume integral equations associated with the scattering problem by 3-D inhomogeneous bodies. A solution technique using a sparse generalized minimal residual method is demonstrated for the analysis of scattering by conducting bodies of revolution, which is described by a vector integro-differential equation. (Abstract shortened by UMI.)... |
