In this paper, the precorrected-FFT method is used to solve the electromagnetic scattering from two-dimensional cavities of arbitrary shape. The integral equation is discretized by the method of moments and the resultant matrix equation is solved iteratively by the generalized conjugate residual method. Instead of directly computing the matrix-vector multiplication, which requires N² operations, this approach reduces the computation complexity to O(N log N) as well as avoids the storage of large matrices. At the same time, a technique known as the complexifying k is applied to accelerate the convergence of the iterative method in solving this resonance problem. Some examples are considered and excellent agreements of radar cross sections between these computed using the present method and those from the direct solution are observed, demonstrating the feasibility and efficiency of the present method. / Singapore-MIT Alliance (SMA)

This paper presents an accurate and efficient method-of-moments solution of the electrical-field integral equation (EFIE) for large, three-dimensional, arbitrarily shaped objects. In this method, the generalized conjugate residual method (GCR) is used to solve the matrix equation iteratively and the precorrected-FFT technique is then employed to accelerate the matrix-vector multiplication in iterations. The precorrected-FFT method eliminates the need to generate and store the usual square impedance matrix, thus leading to a great reduction in memory requirement and execution time. It is at best an O(N log N) algorithm and can be modified to fit a wide variety of systems with different Green’s functions without excessive effort. Numerical results are presented to demonstrate the accuracy and computational efficiency of the technique. / Singapore-MIT Alliance (SMA)

Dissertation (Ph.D.)--Auburn University,2008. / Abstract. Vita. Includes bibliographic references (p.83-85).

In this thesis, it is demonstrated that the two-dimensional Windowed Fourier Transform (WFT) can be effectively used to analyze the local spectral characteristics of electromagnetic scattering signals in the two-dimensional spatial frequency domain. The WFT is the extension of the Short Time Fourier Transform (STFT), which was originally derived to analyze the local spectral characteristics of one dimensional time functions. Since the WFT focuses on the local spectral behavior of the scattered field, the signal localization maps produced in the spectral domain by the WFT can be used to identify the contributions of the rays, at a given location in space, arising from various scattering mechanisms in high frequency applications.

While exact methods, such as DDA or T-matrix, can be applied to particles withsizes comparable to the wavelength, computational demands mean that they are size limited. For particles much larger than the wavelength, the Geometric Optics approximation can be employed, but in doing so wave effects, such as interference and diffraction, are ignored. In between these two size extremes there exists a need for computational techniques which are capable of handling the wide array of ice crystal shapes and sizes that are observed in cirrus clouds. The Beam Tracing model developed within this project meets these criteria. It combines aspects of geometric optics and physical optics. Beam propagation is handled by Snell's law and the law of reflection. A beam is divided into reflected and transmitted components each time a crystal facet is illuminated. If the incident beam illuminates multiple facets it is split, with a new beam being formed for each illuminated facet. The phase-dependent electric field amplitude of the beams is known from their ampli- tude (Jones) matrices. These are modified by transmission and reflection matrices, whose elements are Fresnel amplitude coefficients, each time a beam intersects a crystal facet. Phase tracing is carried out for each beam by considering the path that its 'centre ray' would have taken. The local near-field is then mapped, via a surface integral formulation of a vector Kirchhoff diffraction approximation, to the far-field. Once in the far-field the four elements of the amplitude matrix are trans- formed into the sixteen elements of the scattering matrix via known relations. The model is discussed in depth, with details given on its implementation. The physical basis of the model is given through a discussion of Ray Tracing and how this leads to the notion of Beam Tracing. The beam splitting algorithm is described for convex particles followed by the necessary adaptations for concave and/or ab- sorbing particles. Once geometric aspects have been established details are given as to how physical properties of beams are traced including: amplitude, phase and power. How diffraction is implemented in the model is given along with a review of existing diffraction implementations. Comparisons are given, first against a modified Ray Tracing code to validate the geometric optics aspects of the model. Then, specific examples are given for the cases of transparent, pristine, smooth hexagonal columns of four different sizes and orientations; a highly absorbing, pristine, smooth hexagonal column and a highly absorbing, indented, smooth hexagonal column. Analysis of two-dimensional and one-dimensional intensity distributions and degree of linear polarisation results are given for each case and compared with results acquired through use of the Amster- dam Discrete-Dipole Approximation (ADDA) code; with good agreement observed. To the author's best knowledge, the Beam Tracer developed here is unique in its ability to handle concave particles; particles with complex structures and the man- ner in which beams are divided into sub-beams of quasi-constant intensity when propagating in an absorbing medium. One of the model's potential applications is to create a database of known particle scattering patterns, for use in aiding particle classification from images taken by the Small Ice Detector (SID) in-situ probe. An example of creating such a database for hexagonal columns is given.

Cette thèse porte sur la diffraction d’une onde plane électromagnétique par une surface lisse parfaitement conductrice (PEC). Elle présente l’analyse des propriétés d’une nouvelle formulation des trois principales équations intégrales de frontières de la théorie de la diffraction électromagnétique (EFIE, MFIE et CFIE). L’idée est d’adapter les équations intégrales conventionnelles à la diffraction d’une onde plane en supposant que la fonction de phase de l’onde plane incidente détermine la fonction de phase de la distribution de courant induit sur la surface.L’idée d’utiliser la phase dans la diffraction d’ondes planes a déjà été étudiée pour les hautes fréquences, notamment dans les thèses de Zhou (1995) et Darrigrand (2002) qui adaptèrent les espaces d’approximation des éléments finis. Dans cette thèse, cependant, nous suivons une formulation plus récente, donnée par Herberthson (2008), où la fonction de phase est incorporée dans la distribution du noyau des opérateurs intégraux.En présentant les versions modifiées de l’EFIE et de la MFIE (dénommées HEFIE et HMFIE)dans des espaces fonctionnels appropriés, nous prouvons ici l’existence d’une solution unique à cette formulation spécifique et présentons une mise en oeuvre pratique originale qui tire parti de l’expérience acquise sur l’EFIE/MFIE. Par la suite, nous explorons une propriété importante offerte par ces nouvelles formulations: la possibilité de réduire le nombre de degrés de liberté requis pour obtenir une solution précise du problème. / This thesis is about the scattering of an electromagnetic plane wave incidenton a perfectly conducting smooth surface. It presents the analysis of the properties of a newformulation of the three principal boundary integral equations of electromagnetic scattering theory(EFIE, MFIE and CFIE). The basic idea is to adapt the conventional integral equations toplane-wave scattering by supposing that the phase function of an incident plane wave determinesthe phase function of the induced boundary current distribution.This idea of using the phase in plane wave scattering has previously been studied in highfrequencyscattering, in particular in the theses by Zhou (1995) and Darrigrand (2002) whoadapt the finite element approximation spaces. In this thesis, though, we follow a more recentformulation, given by Herberthson (2008), where the phase function is incorporated in the kerneldistribution of the integral operators.Presenting the modified version of the EFIE and the MFIE (denoted HEFIE and HMFIE) inappropriate function spaces, we prove the existence of a unique solution to this specific formulationand developp an original practical implementation which takes advantage of the gainedexperience on the EFIE/MFIE. Then, we explore another important property provided by thenew formulations: the possibility to reduce the number of degrees of freedom required to get anaccurate solution of the problem.

Deux pièces de travail sont inclus dans cette thèse. La première partie analyse l'interaction d'une sphère excentrique avec un faisceau incident quelconque formé dans le cadre de généralisé de la théorie de Lorenz-Mie (generalized Lorenz-Mie theory, GLMT). Distributions de contrôle interne, près de la surface, loin des champs dispersés zone ainsi que le comportement de la morphologie dépendant résonances (MDR) dans une sphère excentrique éclairée par un faisceau focalisé guassien sont analysés. Dans la seconde partie, en utilisant l'EBCM, les propriétés de diffusion de lumière autour de l'angle arc pour un ensemble de sphéroïdes dans des orientations aléatoires éclairé par une onde plane sont étudiés. En comparant les paramètres extraits de ces paramètres originaux utilisés dans les expériences de simulation, la sensibilité de la technique d'arc de la sphéricité des gouttelettes non est quantifié. / Two parts of this work are included in this thesis. The first part analyses the interaction of an eccentric particle with an arbitrary incident shaped beam within the generalized Lorenz-Mie theory (GLMT). Distributions of internal, near-surface, far-zone scattered fields as well as the behavior of morphlogy-dependent resonances (MDRs) in an eccentric sphere illuminated by a focused Gaussian beam are analysed. In the second part, by using the ECBM, light scattering properties around the rainbow angle for an ensemble of spheroids in random orientations illuminated by a plane wave are studied. By comparing the extracted parameters with those original parameters used in the simulation experiments, the sensitivity of the rainbow technique to the non-sphericity of droplets is quantified.

Time-domain methods are preferred over their frequency-domain counterparts for solving acoustic and electromagnetic scattering problems since they can produce wide- band data from a single simulation. Among the time-domain methods, time-domain surface integral equation solvers have recently found widespread use because they offer several benefits over differential equation solvers. This dissertation develops several second-kind surface integral equation solvers for analyzing transient acoustic scattering from rigid and penetrable objects and transient electromagnetic scattering from perfect electrically conducting and dielectric objects. For acoustically rigid, perfect electrically conducting, and dielectric scatterers, fully explicit marching-on-in-time schemes are developed for solving time domain Kirchhoff, magnetic field, and scalar potential integral equations, respectively. The unknown quantity (e.g., velocity potential, electric current, or scalar potential) on the scatterer surface is discretized using a higher-order method in space and Lagrange interpolation in time. The resulting system is cast in the form of an ordinary differen- tial equation and integrated in time using a predictor-corrector scheme to obtain the unknown expansion coefficients. The explicit scheme can use the same time step size as its implicit counterpart without sacrificing from the stability of the solution and is much faster under low-frequency excitation (i.e., for large time step size). In addition, low-frequency behavior of vector potential integral equations for perfect electrically conducting scatterers is also investigated in this dissertation. For acoustically penetrable scatterers, presence of spurious interior resonance modes in the solutions of two forms of time domain surface integral equations is investigated. Numerical results demonstrate that the solution of the form that is widely used in the literature is corrupted by the interior resonance modes. But, the amplitude of these modes in the time domain can be suppressed by increasing the accuracy of discretization especially in time. On the other hand, the proposed one in the combined form shows a resonance-free performance verified via numerical experiments. In addition to providing detailed formulations of these solvers, the dissertation presents numerical examples, which demonstrate the solvers’ accuracy, efficiency, and applicability in real-life scenarios.

No description available.

A numerical study of electromagnetic scattering by one-dimensional perfectly conducting randomly rough surfaces with an ocean-like Pierson-Moskowitz spectrum is presented. Simulations are based on solving the Magnetic Field Integral Equation (MFIE) using the numerical technique called the Method of Ordered Multiple Interactions (MOMI). The study focuses on the application and validation of this integral equation-based technique to scattering at low grazing angles and considers other aspects of numerical simulations crucial to obtaining correct results in the demanding low grazing angle regime. It was found that when the MFIE propagator matrix is used with zeros on its diagonal (as has often been the practice) the results appear to show an unexpected sensitivity to the sampling interval. This sensitivity is especially pronounced in the case of horizontal polarization and at low grazing angles. We show - both numerically and analytically - that the problem lies not with the particular numerical technique used (MOMI) but rather with how the MFIE is discretized. It is demonstrated that the inclusion of so-called "curvature terms" (terms that arise from a correct discretization procedure and are proportional to the second surface derivative) in the diagonal of the propagator matrix eliminates the problem completely. A criterion for the choice of the sampling interval used in discretizing the MFIE based on both electromagnetic wavelength and the surface spectral cutoff is established. The influence of the surface spectral cutoff value on the results of scattering simulations is investigated and a recommendation for the choice of this spectral cutoff for numerical simulation purposes is developed. Also studied is the applicability of the tapered incident field at low grazing incidence angles. It is found that when a Gaussian-like taper with fixed beam waist is used there is a characteristic pattern (anomalous jump) in the calculated average backscattered cross section at incidence angles close to grazing that indicates a failure of this approximate (non-Maxwellian) taper. This effect is very pronounced for the horizontal polarization and is not observed for vertical polarization and the differences are explained. Some distinctive features associated with the taper failure are visible in the surface current (solution to the MFIE) as well. Based on these findings we are able to refine one of the previously proposed criteria that relate the taper waist to the angle of incidence and demonstrate its robustness. / Ph. D.