A new full-wave surface impedance integral equation method is presented for three-dimensional arbitrary-shaped interconnect parasitic extraction in layered media. Various new ways of applying voltage and current excitations for electromagnetic-circuit simulation are introduced. A new algorithm is proposed for matrix formation of electromagnetic-circuit simulation, low frequency solution and layered media so that it can be easily integrated to a Rao-Wilton-Glisson based method of moment code. Two mixed potential integral equation forms of the electric field integral equation are adapted along with the Michalski-Mosig formulations for layered kernels to model electromagnetic interactions of interconnects in layered media over a conducting substrate. The layered kernels are computed directly for controllable accuracy. The proposed methods are validated against existing methods for both electromagnetic and electromagnetic-circuit problems.

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.

In this dissertation, a hybrid volume and surface integral equation is used to solve scattering problems. It is implemented with RWG basis on the surface and the edge basis in the volume. Numerical results shows the correctness of the hybrid VSIE in inhomogeneous medium. The MLFMM method is also implemented for the new VSIEs. Further more, a synthetic apature radar imaging method is used in a 2D microwave imaging for complex objects. With the mono-static and bi-static interpolation scheme, a 2D FFT is applied for the imaging with the data simulated with VSIE method. Then we apply a background cancelling scheme to improve the imaging quality for the targets in interest. Numerical results shows the feasibility of applying the background canceling into wider applications.

Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: The Method of Moments (MoM) is routinely used for the numerical solution of electromagnetic surface integral equations. Solution errors are inherent to any numerical computational method, and error estimators can be effectively employed to reduce and control these errors. In this thesis, gradient recovery techniques of the Finite Element Method (FEM) are formulated within the MoM context, in order to recover a higher-order charge of a Rao-Wilton-Glisson (RWG) MoM solution. Furthermore, a new recovery procedure, based specifically on the properties of the RWG basis functions, is introduced by the author. These recovered charge distributions are used for a posteriori error estimation of the charge. It was found that the newly proposed charge recovery method has the highest accuracy of the considered recovery methods, and is the most suited for applications within recovery based error estimation. In addition to charge recovery, the possibility of recovery procedures for the MoM solution current are also investigated. A technique is explored whereby a recovered charge is used to find a higher-order divergent current representation. Two newly developed methods for the subsequent recovery of the solenoidal current component, as contained in the RWG solution current, are also introduced by the author. A posteriori error estimation of the MoM current is accomplished through the use of the recovered current distributions. A mixed second-order recovered current, based on a vector recovery procedure, was found to produce the most accurate results. The error estimation techniques developed in this thesis could be incorporated into an adaptive solver scheme to optimise the solution accuracy relative to the computational cost. / AFRIKAANSE OPSOMMING: Die Moment Metode (MoM) vind algemene toepassing in die numeriese oplossing van elektromagnetiese oppervlak integraalvergelykings. Numeriese foute is inherent tot die prosedure: foutberamingstegnieke is dus nodig om die betrokke foute te analiseer en te reduseer. Gradiënt verhalingstegnieke van die Eindige Element Metode word in hierdie tesis in die MoM konteks geformuleer. Hierdie tegnieke word ingespan om die oppervlaklading van 'n Rao-Wilton-Glisson (RWG) MoM oplossing na 'n verbeterde hoër-orde voorstelling te neem. Verder is 'n nuwe lading verhalingstegniek deur die outeur voorgestel wat spesifiek op die eienskappe van die RWG basis funksies gebaseer is. Die verhaalde ladingsverspreidings is geïmplementeer in a posteriori fout beraming van die lading. Die nuut voorgestelde tegniek het die akkuraatste resultate gelewer, uit die groep verhalingstegnieke wat ondersoek is. Addisioneel tot ladingsverhaling, is die moontlikheid van MoM-stroom verhalingstegnieke ook ondersoek. 'n Metode vir die verhaling van 'n hoër-orde divergente stroom komponent, gebaseer op die verhaalde lading, is geïmplementeer. Verder is twee nuwe metodes vir die verhaling van die solenodiale komponent van die RWG stroom deur die outeur voorgestel. A posteriori foutberaming van die MoM-stroom is met behulp van die verhaalde stroom verspreidings gerealiseer, en daar is gevind dat 'n gemengde tweede-orde verhaalde stroom, gebaseer op 'n vektor metode, die beste resultate lewer. Die foutberamingstegnieke wat in hierdie tesis ondersoek is, kan in 'n aanpasbare skema opgeneem word om die akkuraatheid van 'n numeriese oplossing, relatief tot die berekeningskoste, te optimeer.

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.

Estimation of the Radar Cross Section of large inhomogeneous scattering objects such as composite aircrafts, ships and biological bodies at high frequencies has posed large computational challenge. The detection of scattering from wake vortex leading to detection and possible identification of low observable aircrafts also demand the development of computationally efficient and rigorous numerical techniques. Amongst the various methods deployed in Computational Electromagnetics, the Method of Moments predicts the electromagnetic characteristics accurately. Method of Moments is a rigorous method, combined with an array of modeling techniques such as triangular patch, cubical cell and tetrahedral modeling. Method of Moments has become an accurate technique for solving electromagnetic problems from complex shaped homogeneous and inhomogeneous objects. One of the drawbacks of Method of Moments is the fact that it results into a dense matrix, the inversion of which is a computationally complex both in terms of physical memory and compute power. This has been the prime reason for the Method of Moments hitherto remaining as a low frequency method. With recent advances in supercomputing, it is possible to extend the range of Method of Moments for Radar Cross Section computation of aircraft like structures and radiation characteristic of antennas mounted on complex shaped bodies at realistic frequencies of practical interest. This thesis is a contribution in this direction. The main focus of this thesis is development of parallel Method of Moments solvers, applied to solve real world electromagnetic wave scattering and radiation problems from inhomogeneous objects. While the methods developed in this thesis are applicable to a variety of problems in Computational Electromagnetics as shown by illustrative examples, in specific, it has been applied to compute the Radar Cross Section enhancement due to acoustic disturbances and flow inhomogeneities from the wake vortex of an aircraft, thus exploring the possibility of detecting stealth aircraft. Illustrative examples also include the analysis of antenna mounted on an aircraft. In this thesis, first the RWG basis functions have been used in Method of Moments procedure, for solving scattering problems from complex conducting structures such as aircraft and antenna(s) mounted on airborne vehicles, of electrically large size of about 45 and 0.76 million unknowns. Next, the solver using SWG basis functions with tetrahedral and pulse basis functions with cubical modeling have been developed to solve scattering from 3D inhomogeneous bodies. The developed codes are validated by computing the Radar Cross Section of spherical homogeneous and inhomogeneous layered scatterers, lossy dielectric cylinder with region wise inhomogeneity and high contrast dielectric objects. Aerodynamic flow solver ANSYS FLUENT, based on Finite Volume Method is used to solve inviscid compressible flow problem around the aircraft. The gradients of pressure/density are converted to dielectric constant variation in the wake region by using empirical relation and interpolation techniques. Then the Radar Cross Section is computed from the flow inhomogeneities in the vicinity of a model aircraft and beyond (wake zone) using the developed parallel Volume Surface Integral Equation using Method of Moments and investigated more rigorously. Radar Cross Section enhancement is demonstrated in the presence of the flow inhomogeneities and detectability is discussed. The Bragg scattering that occurs when electromagnetic and acoustic waves interact is also discussed and the results are interpreted in this light. The possibility of using the scattering from wake vortex to detect low visible aircraft is discussed. This thesis also explores the possibility of observing the Bragg scattering phenomenon from the acoustic disturbances, caused by the wake vortex. The latter sets the direction for use of radars for target identification and beyond target detection. The codes are parallelized using the ScaLAPACK and BiCG iterative method on shared and distributed memory machines, and tested on variety of High Performance Computing platforms such as Blue Gene/L (22.4TF), Tyrone cluster, CSIR-4PI HP Proliant 3000 BL460c (360TF) and CRAY XC40 machines. The parallelization speedup and efficiency of all the codes has also been shown.

No description available.