Advanced Integral Equation and Hybrid Methods for the Efficient Analysis of General Waveguide and Antenna Structures

Three new numerical methods for the calculation of passive waveguide and antenna structures are presented in this work. They are designed to be used within a comprehensive hybrid CAD tool for the efficient analysis of those building blocks for which the fast mode-matching/2-D finite element technique cannot be applied. The advanced algorithms introduced here are doubly higher order, that is higher order basis functions are considered for current/field modeling whereas geometry discretization is performed with triangular/tetrahedral elements of higher polynomial degree

Fast methods for inverse wave scattering problems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 125-137).Inverse wave scattering problems arise in many applications including computerized/diffraction tomography, seismology, diffraction/holographic grating design, object identification from radar singals, and semiconductor quality control. Efficient algorithms exist for some inverse wave scattering problems in the low- and high-frequency regime or with weak scatterers. However, inverse wave scattering problems in the resonance regime with strong scatterers still pose many challenges. This thesis proposes algorithms for inverse wave scattering problems in the resonance regime with strong scatterers. These problems are part of, for instance, grating design, object identification, and semiconductor quality control. The proposed methods are (a) a spectrally convergent Nyström method for periodic structures in 2-D; (b) a fast Jacobian approximation method accompanying a Nyström method; (c) a fast and accurate method for evaluating the potential integrals in the 3-D mixed-potential integral operator with the Rao-Wilton-Glisson basis function; and (d) optimization with parameterized reduced-order models. The Nyström method and the method to evaluate the potential integrals accelerate scattered field evaluations by solving integral equations efficiently. The Jacobian approximation method and optimization with parameterized reduced-order models efficiently couple algorithms to evaluate scattered fields due to a guess of the scatterer and optimization methods to improve the guess. The Nyström and the Jacobian approximation methods are used to identify the parameters characterizing a periodic dielectric grating in 2-D. The method to evaluate the potential integrals and optimization with parameterized reduced-order models are applied to the problem of identifying simple discrete geometries in 3-D.by Jung Hoon Lee.Ph.D

Computational aspects of electromagnetic NDE phenomena

The development of theoretical models that characterize various physical phenomena is extremely crucial in all engineering disciplines. In nondestructive evaluation (NDE), theoretical models are used extensively to understand the physics of material/energy interaction, optimize experimental design parameters and solve the inverse problem of defect characterization. This dissertation describes methods for developing computational models for electromagnetic NDE applications. Two broad classes of issues that are addressed in this dissertation are related to (i) problem formulation and (ii) implementation of computers;The two main approaches for solving physical problems in NDE are the differential and integral equations. The relative advantages and disadvantages of the two approaches are illustrated and models are developed to simulate electromagnetic scattering from objects or inhomogeneities embedded in multilayered media which is applicable in many NDE problems. The low storage advantage of the differential approach and the finite solution domain feature of the integral approach are exploited. Hybrid techniques and other efficient modeling techniques are presented to minimize the storage requirements for both approaches;The second issue of computational models is the computational resources required for implementation. Implementations on conventional sequential computers, parallel architecture machines and more recent neural computers are presented. An example which requires the use of massive parallel computing is given where a probability of detection model is built for eddy current testing of 3D objects. The POD model based on the finite element formulation is implemented on an NCUBE parallel computer. The linear system of equations is solved using direct and iterative methods. The implementations are designed to minimize the interprocessor communication and optimize the number of simultaneous model runs to obtain a maximum effective speedup;Another form of parallel computing is the more recent neurocomputer which depends on building an artificial neural network composed of numerous simple neurons. Two classes of neural networks have been used to solve electromagnetic NDE inverse problems. The first approach depends on a direct solution of the governing integral equation and is done using a Hopfield type neural network. Design of the network structure and parameters is presented. The second approach depends on developing a mathematical transform between the input and output space of the problem. A multilayered perceptron type neural network is invoked for this implementation. The network is augmented to build an incremental learning network which is motivated by the dynamic and modular features of the human brain

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 2

Two families of parametrized mixed variational principles for linear electromagnetodynamics are constructed. The first family is applicable when the current density distribution is known a priori. Its six independent fields are magnetic intensity and flux density, magnetic potential, electric intensity and flux density and electric potential. Through appropriate specialization of parameters the first principle reduces to more conventional principles proposed in the literature. The second family is appropriate when the current density distribution and a conjugate Lagrange multiplier field are adjoined, giving a total of eight independently varied fields. In this case it is shown that a conventional variational principle exists only in the time-independent (static) case. Several static functionals with reduced number of varied fields are presented. The application of one of these principles to construct finite elements with current prediction capabilities is illustrated with a numerical example

13th Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School, Monterey, CA, March 17-21, 1997, Conference Proceedings Volumes I & II

Includes Volumes 1 &

Numerical methods for electromagnetic wave propagation and scattering in complex media

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Vita.Includes bibliographical references (p. 227-242).Numerical methods are developed to study various applications in electromagnetic wave propagation and scattering. Analytical methods are used where possible to enhance the efficiency, accuracy, and applicability of the numerical methods. Electromagnetic induction (EMI) sensing is a popular technique to detect and discriminate buried unexploded ordnance (UXO). Time domain EMI sensing uses a transient primary magnetic field to induce currents within the UXO. These currents induce a secondary field that is measured and used to determine characteristics of the UXO. It is shown that the EMI response is difficult to calculate in early time when the skin depth is small. A new numerical method is developed to obtain an accurate and fast solution of the early time EMI response. The method is combined with the finite element method to provide the entire time domain response. The results are compared with analytical solutions and experimental data, and excellent agreement is obtained. A fast Method of Moments is presented to calculate electromagnetic wave scattering from layered one dimensional rough surfaces. To facilitate the solution, the Forward Backward method with Spectral Acceleration is applied. As an example, a dielectric layer on a perfect electric conductor surface is studied. First, the numerical results are compared with the analytical solution for layered flat surfaces to partly validate the formulation. Second, the accuracy, efficiency, and convergence of the method are studied for various rough surfaces and layer permittivities. The Finite Difference Time Domain (FDTD) method is used to study metamaterials exhibiting both negative permittivity and permeability in certain frequency bands.(cont.) The structure under study is the well-known periodic arrangement of rods and split-ring resonators, previously used in experimental setups. For the first time, the numerical results of this work show that fields propagating inside the metamaterial with a forward power direction exhibit a backward phase velocity and negative index of refraction. A new metamaterial design is presented that is less lossy than previous designs. The effects of numerical dispersion in the FDTD method are investigated for layered, anisotropic media. The numerical dispersion relation is derived for diagonally anisotropic media. The analysis is applied to minimize the numerical dispersion error of Huygens' plane wave sources in layered, uniaxial media. For usual discretization sizes, a typical reduction of the scattered field error on the order of 30 dB is demonstrated. The new FDTD method is then used to study the Angular Correlation Function (ACF) of the scattered fields from continuous random media with and without a target object present. The ACF is shown to be as much as 10 dB greater when a target object is present for situations where the target is undetectable by examination of the radar cross section only.by Christopher D. Moss.Ph.D

Electromagnetic Scattering from a Cavity in a Ground Plane: Theory and Experiment

The electromagnetic scattering from an arbitrarily shaped open cavity embedded in a perfectly conducting, infinite ground plane is examined. The cavity is filled with a linear, isotropic, homogeneous material. The fields in the cavity interior and above the ground plane are expressed in terms of the tangential fields on the cavity surface and aperture. A coupled set of three integral equations is developed governing the tangential fields on the aperture and cavity surface. The support of the unknown tangential fields is finite. A moment-method based algorithm to approximate the solution to the integral equations for axisymmetric geometries is developed. The unknown tangential fields are expanded using piecewise-linear functions in the elevation plane and complex exponentials in the azimuth plane. Orthogonality is exploited to reduce the size of the matrix. The algorithm yields a well-conditioned numerical solution. The solution obeys the edge condition at the aperture rim. The integral equations are uniquely solvable at frequencies where other integral equation-based techniques admit spurious solutions. Radar cross section calculations are compared to experimental measurements of full-scale physical models. Results show that an open cavity can serve as an effective radar cross section enhancement device

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 1

This research program has dealt with the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements; (2) finite element modeling of the electromagnetic problem; (3) coupling of thermal and mechanical effects; and (4) computer implementation and solution of the superconductivity transition problem. The research was carried out over the period September 1988 through March 1993. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles; (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements; and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects; and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The grant has fully supported the thesis work of one doctoral student (James Schuler, who started on January 1989 and completed on January 1993), and partly supported another thesis (Carmelo Militello, who started graduate work on January 1988 completing on August 1991). Twenty-three publications have acknowledged full or part support from this grant, with 16 having appeared in archival journals and 3 in edited books or proceedings