abstract: We present fast and robust numerical algorithms for 3-D scattering from perfectly electrical conducting (PEC) and dielectric random rough surfaces in microwave remote sensing. The Coifman wavelets or Coiflets are employed to implement Galerkin’s procedure in the method of moments (MoM). Due to the high-precision one-point quadrature, the Coiflets yield fast evaluations of the most off-diagonal entries, reducing the matrix fill effort from O(N^2) to O(N). The orthogonality and Riesz basis of the Coiflets generate well conditioned impedance matrix, with rapid convergence for the conjugate gradient solver. The resulting impedance matrix is further sparsified by the matrix-formed standard fast wavelet transform (SFWT). By properly selecting multiresolution levels of the total transformation matrix, the solution precision can be enhanced while matrix sparsity and memory consumption have not been noticeably sacrificed. The unified fast scattering algorithm for dielectric random rough surfaces can asymptotically reduce to the PEC case when the loss tangent grows extremely large. Numerical results demonstrate that the reduced PEC model does not suffer from ill-posed problems. Compared with previous publications and laboratory measurements, good agreement is observed. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2016

abstract: Asymptotic and Numerical methods are popular in applied electromagnetism. In this work, the two methods are applied for collimated antennas and calibration targets, respectively. As an asymptotic method, the diffracted Gaussian beam approach (DGBA) is developed for design and simulation of collimated multi-reflector antenna systems, based upon Huygens principle and independent Gaussian beam expansion, referred to as the frames. To simulate a reflector antenna in hundreds to thousands of wavelength, it requires 1E7 - 1E9 independent Gaussian beams. To this end, high performance parallel computing is implemented, based on Message Passing Interface (MPI). The second part of the dissertation includes the plane wave scattering from a target consisting of doubly periodic array of sharp conducting circular cones by the magnetic field integral equation (MFIE) via Coiflet based Galerkin's procedure in conjunction with the Floquet theorem. Owing to the orthogonally, compact support, continuity and smoothness of the Coiflets, well-conditioned impedance matrices are obtained. Majority of the matrix entries are obtained in the spectral domain by one-point quadrature with high precision. For the oscillatory entries, spatial domain computation is applied, bypassing the slow convergence of the spectral summation of the non-damping propagating modes. The simulation results are compared with the solutions from an RWG-MLFMA based commercial software, FEKO, and excellent agreement is observed. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012