Doctor of Philosophy / Department of Electrical and Computer Engineering / Kenneth H. Carpenter / A computer simulation of transient current density distributions in thin conductors was developed using a time-stepped implementation of the integral equation method on a finite element mesh. A study of current distributions in thin conductors was carried out using AC analysis methods. The study of the AC current density distributions was used to develop a circuit theory model for the thin conductor which was then used to determine the nature of its transient response. This model was used to support the design and evaluation of the transient current density solver. A circuit model for strip lines was made using the Partial Inductance Method to allow for simulations with the SPICE circuit solver. Magnetic probes were designed and tested that allow for physical measurements of voltages induced by the magnetic field generated by the current distributions in the strip line. A comparison of the measured voltages to simulated values from SPICE was done to validate the SPICE model. This model was used to validate the finite-integration model for the same strip line. Formulation of the transient current density distribution problem is accomplished by the superposition of a source current and an eddy current distribution on the same space. The mathematical derivation and implementation of the time-stepping algorithm to the finite element model is explicitly shown for a surface mesh with triangular elements. A C++ computer program was written to solve for the total current density in a thin conductor by implementing the time-stepping integral formulation. Evaluation of the finite element implementation was made regarding mesh size. Finite element meshes of increasing node density were simulated for the same structure until a smooth current density distribution profile was observed. The transient current density solver was validated by comparing simulations with AC conduction and transient response simulations of the SPICE model. Transient responses are compared for inputs at different frequencies and for varying time steps. This program is applied to thin conductors of irregular shape.

An efficient integral equation method based on a method of moment (MoM) discretization of the Mixed-Potential Integral Equation (MPIE) for the analysis of 2.5D or 3D planar microwave circuits is presented. The robust Discrete Complex Image Method (DCIM) is employed to approximate the Greens functions in layered media for horizontal and vertical sources of fields, where closed-form formulations of the z-integrations are derived in the spectral domain. Meanwhile, an efficient and accurate numerical integration technique based on the Khayat-Wilton transform is used to integrate functions with 1/R singularities and near singularities. The fast iterative solver - Quadrature Sampled Pre-Corrected Fast Fourier Transform (QSPCFFT) - is associated with the MoM formulation to analyze electrically large, dense and complex microwave circuits.

Novel integral-equation methods for efficiently solving electromagnetic problems that involve more than a single length scale of interest in complex backgrounds are presented. Such multi-scale electromagnetic problems arise because of the interplay of two distinct factors: the structure under study and the background medium. Both can contain material properties (wavelengths/skin depths) and geometrical features at different length scales, which gives rise to four types of multi-scale problems: (1) twoscale, (2) multi-scale structure, (3) multi-scale background, and (4) multi-scale-squared problems, where a single-scale structure resides in a different single-scale background, a multi-scale structure resides in a single-scale background, a single-scale structure resides in a multi-scale background, and a multi-scale structure resides in a multi-scale background, respectively. Electromagnetic problems can be further categorized in terms of the relative values of the length scales that characterize the structure and the background medium as (a) high-frequency, (b) low-frequency, and (c) mixed-frequency problems, where the wavelengths/skin depths in the background medium, the structure’s geometrical features or internal wavelengths/skin depths, and a combination of these three factors dictate the field variations on/in the structure, respectively. This dissertation presents several problems arising from geophysical exploration and microwave chemistry that demonstrate the different types of multi-scale problems encountered in electromagnetic analysis and the computational challenges they pose. It also presents novel frequency-domain integral-equation methods with proper Green function kernels for solving these multi-scale problems. These methods avoid meshing the background medium and finding fields in an extended computational domain outside the structure, thereby resolving important complications encountered in type 3 and 4 multi-scale problems that limit alternative methods. Nevertheless, they have been of limited practical use because of their high computational costs and because most of the existing ‘fast integral-equation algorithms’ are not applicable to complex Green function kernels. This dissertation introduces novel FFT, multigrid, and FFT-truncated multigrid algorithms that reduce the computational costs of frequency-domain integral-equation methods for complex backgrounds and enable the solution of unprecedented type 3 and 4 multi-scale problems. The proposed algorithms are formulated in detail, their computational costs are analyzed theoretically, and their features are demonstrated by solving benchmark and challenging multi-scale problems. / text

This study is to develop a 2D fully nonlinear numerical wave tank used to investigate the wave-induced dynamic properties of a dual pontoon floating structure (DPFS) with a liquid container on the top. The nonlinear numerical wave tank, developed based on the velocity potential function and the boundary element method (BEM), is to simulate dynamic properties including sway, heave, roll, and tension response. In addition, a physical model of the dual floating pontoon is tested in a hydrodynamic wave tank to validate the numerical model for simulation of wave and structure interaction. In the numerical model, a boundary integral equation method (BIEM) with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and a cubic spline scheme. The second-order Stokes wave theory is used to generate the velocity flux on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected waves. Acceleration potential method and modal decomposition method are adopted to solve the unsteady potential functions £X1,t and £X2,t, while the system of motion equation is established according to Newton's 2nd law. Finally, the RK4 is applied to predict the motion of the platform, and the variation of free surface. As for the hydrodynamic laboratory model test, an image process scheme is applied to trace the floating structure motion and the variation of water surface inside the sloshing tank, while the mooring tension is measured by a load cell and stored in a data logger. The comparisons of numerical simulations and experimental data indicate that the numerical predictions are larger than measurements especially near the resonance frequency. This discrepancy is probably due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained through a damping ratio (£a=C/Ccr=0.02) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significantly reduced and close to the measurements. Therefore, the suitable value of the damping ratio for the floating platform is £a=0.02. Then the numerical model with a damping ratio is applied to investigate the dynamic properties of the floating platform for different arrangements, including different mooring angle, spring constant, spacing, and the liquid container. Results demonstrate that the resonant frequency of each mode, responses of body motion and mooring tensions change along with the settings. As a whole, the platform with smaller mooring angle, longer spacing between the pontoons, higher water depth and wider width of the liquid container has relatively stable body motions and less mooring tension. Finally, the comparisons of the effects of random and regular waves on the floating structure illustrate that the variation of water surface in the liquid container is much severe in random waves than in regular waves such that the interaction between liquid and floating structure is more chaotic and thus reduces the amplitude of each response mode. As a result, the mooring tensions for random waves become much gentler than the regular waves. Key words: Boundary integral equation method; fully nonlinear numerical wave tank; dual pontoon floating structure

In this thesis, we have compared between dual-core fiber coupler with photonic crystal fiber coupler. From Surface Integral Equation Method derived from Maxwell¡¦s equations, we can simulate tapered fiber coupler, dual-core fiber coupler and photonic crystal fiber coupler. By analyzing the propagating characteristics and performance of these couplers, we hope to discuss between their advantages and dis-advantages. We have found that at the same parameters, conventional fiber coupler¡¦s coupling length is roughly half compared to photonic crystal coupler. In terms of bandwidth, photonic crystal coupler aided by air-hole tuning can achieve multiples times larger than conventional fiber coupler. So, we believe that in communication networks with a lust of bandwidth, photonic crystal coupler can definitely live up its expectations.

A single-mode fused biconical 2¡Ñ2 coupler for polarization beamsplitting is fabricated in this thesis. We use simple fused and tapered method to fabricate the polarization beamsplitter(PBS) stably, and then we can get polarization maintaining in the output fibers. Without changing the manufacturing process, we design the device with special combination of fabrication parameters. We have achieved an extinction ratio of 25.78dB at the throughput port and 27.16dB at the coupled port. A usable spectral window as broad as 37nm and 27nm with an extinction ratio larger than 15dB for both ports is obtained. The excess loss is about 0.3dB. Based on a full-wave numerical approach, the performance of the PBS can be well modeled. We get good agreement between the measured and simulated results.

This paper is to investigate the wave-induced dynamic properties of the floating platform for cage aquaculture. Considering the calculation efficiency and its applicability, this problem is simplified by: (1) assuming the flow field is inviscid, incompressible and irrotational; (2) the form drag and inertia drag on the fish net is calculated by the modified Morison equation (or Morison type equation of relative motion), including the material and geometric properties; (3) the moorings is treated as a symmetric linear spring system and the influence of hydrodynamic forces on the mooring lines is neglected; and (4) the net-volume is assumed as un-deformable to avoid the inversely prolonging computing time because the mass of fish net with is too light comparing with the mass of floating platform and cause the marching time step tremendously small to reach the steady-state condition which may lead to larger numerical errors (e.g. truncation errors) in computation. The BIEM with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and the cubic spline scheme. The second-order Stokes wave theory is adopted to give the velocity on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected wave energy. The velocity and acceleration fields should be solved simultaneously in order to obtain the wave-induced dynamic property of the floating platform. Thus, both the acceleration potential method and modal decomposition method are adopted to solve the wave forces on the floating body, while the wave forces on the fish net are calculated by the modified Morison equation. According to Newton¡¦s second law, the total forces on the gravity center of the floating platform form the equation of motion. Finally, the RK4 is applied to predict the displacement and velocity of the platform. Firstly, the NWT is validated by comparing the wave elevation, internal velocity and acceleration with those from the second-order Stokes wave theory. Moreover, the numerical damping zone is suitable for long time simulation with a wide range of wave depth. The simulated results on wave-body interactions of fixed or freely floating body also indicate good agreement with those of other published results. Secondly, in the case of the interaction of waves and the floating platform, the simulated results show well agreement with experimental data, except at the vicinity of resonant frequency of roll and heave motions. This discrepancy is due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained by a damping ratio (£i=0.1 ) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significant reduction and close to the experimental data. Moreover, the results are also consistent well with experiments in different wave height, mooring angle, water depth either with or without fish net. Therefore, the suitable value of the damping ratio for the floating platform is £i=0.1. Finally, the present model is applied to investigate the dynamic properties of the floating platform under different draft, width, spacing, spring constant, mooring angle and depth of fish net. Results reveal that the resonant frequency and response of body motion, mooring force, reflection and transmission coefficients and wave energy will be changed. According to the resonant response, the platform with shallower draft, larger width, longer spacing between two pontoons, smaller spring constants, or deeper depth of fish net has more stable body motions and smaller mooring forces. Irregular wave cases are presented to illustrate the relationship with the regular wave cases. Results indicate that the dynamic responses of body motion and the reflection coefficient in irregular waves have similar trend with regular waves. However, in the irregular wave cases, the resonant frequency is moved to the higher frequency. Similarly, resonant response function is smaller but wider, which is due to the energy distribution in the wave spectrum.

La méthode PEEC est connue comme une bonne méthode pour la modélisation des interconnexions électriques dans les domaines de l’électronique de puissance et l’électrotechnique. Elle s'applique à une large gamme de dispositifs : circuits imprimés, bus-barres, conducteurs massifs. Elle est particulièrement bien adaptée pour la modélisation de régions conductrices du type filaire. Cependant, elle est requise d’un maillage structuré(discrétisation des géométries en quadrangles) et l’approche est limitée en fréquence (grande épaisseur de peau). Enfin, il semble actuellement difficile d’envisager la modélisation de conducteurs volumiques dans une formulation PEEC standard.Cette thèse développe des formulations intégrales en utilisant des éléments de facette afin d’lever des verrous de la méthode PEEC standard évoqués ci-dessus. Elle constitue de fait une généralisation de la méthode PEEC standard par la prise en compte de maillages non structurés (volumique et surfacique) et la prise en compte de notion de régions minces à faible épaisseur de peau.Les applications visées sont la modélisation de systèmes de conducteurs complexes (des régions non simplement connexes) en prenant en compte des connexions entre des régions (volumique/filaire, surfacique/filaire,volumique/surfacique et surfacique/surfacique). / The PEEC method is known as a good method for modeling electrical connections in the domains of powerelectronics and electrical engineering. It applies to a wide range of devices: printed circuits, bus-bars, solidconductors. It is particularly well adapted for modeling the wire type conductive regions. However, it is requireda structured mesh (discretization geometries quadrangles) and this approach is limited in frequency (high skindepth). Finally, it now seems difficult to envisage modeling of the volume conductors in standard PEECformulation.This thesis develops integrals formulations using facet elements to improve the above mentioned limitations ofthe standard PEEC method. It is in fact a generalization of the standard PEEC method by taking into accountunstructured meshes (volume and surface) and taking into account the notion of thin region with a small skindepth.The applications are the modeling of complex systems of conductors (non-simply connected regions) taking intoaccount the connections between regions (volume / wireframe, surface / wired volume / surface and surface /surface).

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Le travail de cette thèse est consacré à l’étude et l’optimisation d’un cas particulier de la diffusion des ondes électromagnétiques. Elle porte plus particulièrement sur un phénomène appelé le « jet photonique ou jet électromagnétique (jet EM)». Il s’agit d’un faisceau de lumière étroit et concentré en champ proche avec des caractéristiques physiques remarquables. Dans ce travail, un guide d’onde terminé par un embout de forme particulière est utilisé pour générer le jet photonique. Cette thèse a pour objectif l’étude, la caractérisation expérimentale et l’optimisation de jets photoniques pour des applications dans le domaine optique et hyperfréquences. Une méthode robuste et rapide a été développée pour calculer le champ électromagnétique généré par un objet diélectrique ou en sortie d’un guide d'onde avec un embout de forme particulière. Elle est basée sur la Méthode d'Equation Intégrale aux Frontière (MEIF) qui utilise la seconde identité Green. La caractérisation expérimentale des jets photoniques a été réalisée dans le domaine micro-ondes à des fréquences autour de 30 GHz. La possibilité de générer un jet simple et double en utilisant un guide d’onde à embout a été montrée expérimentalement et théoriquement par la méthode MEIF. Les jets EM simples et doubles ont été utilisés pour la détection d’objets métalliques de taille plus petite que la longueur d’onde et l'imagerie en champ proche à travers des structures optiquement opaques. Une procédure d’optimisation basée sur le couplage entre la MEIF et les algorithmes génétiques a été mise au point afin de générer des jets photoniques avec des caractéristiques a priori bien définie. Des optimisations des jets photoniques générés par un objet diélectrique et en sortie d’un guide d’onde avec embout ont été effectuées pour la micro-gravure laser et l’imagerie HF / The work of this thesis is devoted to the study and optimization of a particular case of the scattering of electromagnetic waves. Particularly, it is about a phenomenon called the "photonic jet or electromagnetic jet (EM jet)". This is a narrow light beam concentrated in near-field with remarkable physical characteristics. In this work, a waveguide terminated by a tip with special form is used to generate the photonic jet. This thesis performs the electromagnetic modeling, the experimental characterization and the optimization of photonic jets for applications in optic and microwave field. A robust and fast method was developed to calculate the electromagnetic field generated by a dielectric object or by a waveguide terminated with a tip. It is based on the boundary integral equation method (BIEM) which uses the second Green identity. Experimental characterization of photonic jets was conducted in the microwave field around 30 GHz. The ability to generate a single and double EM jet using a tipped waveguide has been shown experimentally and theoretically by BEIM method. The single and double EM jets were used for the detection of metal objects with a size smaller than the wavelength and for imaging through opaque structures in near field. An optimization procedure based on the coupling between the BEIM and genetic algorithms has been developed to generate photonic jets with properties well defined. Optimizations of photonic jets generated by a dielectric object and by a tipped waveguide have been realized for laser micro-etching and RF imaging