Applications of Adaptive Integral Method in Electromagnetic Scattering by Large-Scale Composite Media and Finite Arrays.

Ph.DDOCTOR OF PHILOSOPH

FFT and multigrid accelerated integral equation solvers for multi-scale electromagnetic analysis in complex backgrounds

textNovel 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.Electrical and Computer Engineerin

Efficient integral equation based algorithms for parasitic extraction of interconnects with smooth or rough surface

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 187-198).This thesis describes a few efficient parasitic extraction algorithms based on integral equation methods. It has two parts. Part one describes the algorithms used in FastImp, a program for accurate analysis of wide-band electromagnetic effects in very complicated geometries of conductors. The program is based on a recently developed surface integral formulation and a Pre-corrected FFT accelerated iterative method, but includes a new piecewise quadrature panel integration scheme, a new scaling and preconditioning technique as well as a generalized grid interpolation and projection strategy. Computational results are given on a variety of integrated circuit interconnect structures to demonstrate that FastImp is robust and can accurately analyze very complicated geometries of conductors. Part two describes an efficient Stochastic Integral Equation (SIE) Method for computing the mean value and variance of the capacitance of interconnects with random surface roughness in O(Nlog2Ì(N)) time. An ensemble average Green's function is used to account for the surface roughness. A second-order correction scheme is used to improve the accuracy. A sparsification technique based on the Hierarchical Matrix method is proposed to significantly reduce the computational cost. The SIE method avoids the time-consuming Monte Carlo simulations and the discretization of rough surfaces. Numerical experiments show that the results of the new method agree very well with those of Monte Carlo simulations.by Zhenhai Zhu.Ph.D

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

Analysis and design of novel electromagnetic metamaterials

This thesis introduces efficient numerical techniques for the analysis of novel electromagnetic metamaterials. The modelling is based on a Method of Moments modal analysis in conjunction with an interpolation scheme, which significantly accelerates the computations. Triangular basis functions are used that allow for modelling of arbitrary shaped metallic elements. Unlike the conventional methods, impedance interpolation is applied to derive the dispersion characteristics of planar periodic structures. With these techniques, the plane wave and the surface wave responses of fractal structures have been studied by means of transmission coefficients and dispersion diagrams. The multiband properties and the compactness of the proposed structures are presented. Based on this method, novel planar left-handed metamaterials are also proposed. Verifications of the left-handedness are presented by means of full wave simulation of finite planar arrays using commercial software and lab measurement. The structures are simple, readily scalable to higher frequencies and compatible with low-cost fabrication techniques.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Different Approaches of Numerical Analysis of Electromagnetic Phenomena in Shaded Pole Motor with Application of Finite Elements Method

In this paper is used Finite Element Method-FEM for analysis of electromagnetic quantities of small micro motor – single phase shaded pole motor-SPSPM. FEM is widely used numerical method for solving nonlinear partial differential equations with variable coefficients. For that purpose motor model is developed with exact geometry and material’s characteristics. Two different approaches are applied in FEM analysis of electromagnetic phenomena inside the motor: magneto-static where all electromagnetic quantities are analysed in exact moment of time meaning frequency f=0 Hz and timeharmonic magnetic approach where the magnetic field inside the machine is time varying, meaning frequency f=50 Hz. Obtained results are presented and compared with available analytical result

Review on Computational Electromagnetics

Computational electromagnetics (CEM) is applied to model the interaction of electromagnetic fields with the objects like antenna, waveguides, aircraft and their environment using Maxwell equations.  In this paper the strength and weakness of various computational electromagnetic techniques are discussed. Performance of various techniques in terms accuracy, memory and computational time for application specific tasks such as modeling RCS (Radar cross section), space applications, thin wires, antenna arrays are presented in this paper

Efficient numerical algorithms for surface formulations of mathematical models for biomolecule analysis and design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 179-183).This thesis presents a set of numerical techniques that extend and improve computational modeling approaches for biomolecule analysis and design. The presented research focuses on surface formulations of modeling problems related to the estimation of the energetic cost to transfer a biomolecule from the gas phase to aqueous solution. The thesis discusses four contributions to modeling biomolecular interactions. First, the thesis presents an approach to allow accurate discretization of the most prevalent mathematical definitions of the biomolecule-solvent interface; also presented are a number of accurate techniques for numerically integrating possibly singular functions over the discretized surfaces. Such techniques are essential for solving surface formulations numerically. The second part of the thesis presents a fast multiscale numerical algorithm, FFTSVD, that efficiently solves large boundary-element method problems in biomolecule electrostatics. The algorithm synthesizes elements of other popular fast algorithms to achieve excellent efficiency and flexibility. The third thesis component describes an integral-equation formulation and boundary-element method implementation for biomolecule electrostatic analysis.(cont.) The formulation and implementation allow the solution of complicated molecular topologies and physical models. Furthermore, by applying the methods developed in the first half of the thesis, the implementation can deliver superior accuracy for competitive performance. Finally, the thesis describes a highly efficient numerical method for calculating a biomolecular charge distribution that minimizes the free energy' change of binding to another molecule. The approach, which represents a novel PDE-constrained methodology, builds on well-developed physical theory. Computational results illustrate not only the method's improved performance but also its application to realistic biomolecule problems.by Jaydeep Porter Bardhan.Ph.D

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