| Electromagnetic propagation and scattering problems are important in many application areas such as communications, high-speed circuitry, medical imaging, geophysical remote sensing, nondestructive testing, and radar. This thesis develops several new techniques for the efficient computer solution of such problems.; Most of this thesis deals with the efficient solution of electromagnetic scattering problems formulated as surface integral equations. A standard method of moments (MOM) formulation is used to reduce the problem to the solution of a dense, {dollar}N times N{dollar} matrix equation, where N is the number of surface current unknowns. An iterative solution technique is used, requiring the computation of many matrix-vector multiplications.; Techniques developed for this problem include the ray-propagation fast multipole algorithm (RPFMA), which is a simple, non-nested, physically intuitive technique based on the fast multipole method (FMM). The RPFMA is implemented for two-dimensional surface integral equations, and reduces the cost of a matrix-vector multiplication from {dollar}O(Nsp2{dollar}) to {dollar}O(Nsp{lcub}4/3{rcub}{dollar}). The use of wavelets is also studied for the solution of two-dimensional surface integral equations. It is shown that the use of wavelets as basis functions produces a MOM matrix with substantial sparsity. However, unlike the RPFMA, the use of a wavelet basis does not reduce the computational complexity of the problem. In other words, the sparse MOM matrix in the wavelet basis still has {dollar}O(Nsp2{dollar}) significant entries. The fast multipole method-fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional rough surface. The resulting algorithm computes a matrix-vector multiply in {dollar}O(N log N{dollar}) operations. This algorithm is shown to be more efficient than another {dollar}O(N log N{dollar}) algorithm, the multi-level fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from two-dimensional random rough surfaces.; Finally, Liao's absorbing boundary condition (ABC) is studied in detail. This is an approximate ABC used to truncate the computational mesh in the finite-difference time-domain (FDTD) method. Unique results, both theoretical and numerical, are presented. |
