published_or_final_version / Physics / Master / Master of Philosophy

A new second order accurate nonuniform grid spacing technique which does not depend on supraconvergence is developed for Finite Difference Time Domain (FDTD) simulation of general three dimensional structures. The technique is useful for FDTD simulations of systems which require finer details in small regions of the simulation space by providing the ability to utilize nonuniform grid spacing. The stability conditions of the new technique are derived and shown to be consistent with uniform grid formulation and the accuracy of the technique is investigated and shown to be second order. The advantage of the new technique is that it allows for greater simulation detail while reducing the computational and memory requirements compared to the current uniform grid FDTD techniques. Additionally, the derivation of the expressions associated with the inclusion of material properties in the FDTD simulation with nonuniform grids is presented allowing for the development of a nonuniform FDTD simulator for general lossy 3D systems associated with on and off chip interconnects, electronic packages and microwave circuits. In order to illustrate the utility of this simulator, time domain electromagnetic simulation of a 3-D lossy interconnect structure associated with a generic surface mount IC package is presented. The time domain currents and fields are computed in the structure to investigate ground bounce, signal degradation, and crosstalk associated with the interconnects and packaging structure. The supply plane conductivities are included in the simulation allowing the observation of the current densities in the power/ground planes as a function of time. Finally, the FDTD simulation tool is proposed and used as a Virtual TDR (V-TDR) to extract the circuit models associated with complex 3D structures. The time domain response of a multiport structure is used to extract the equivalent circuit parameters to characterize the multiport by using the multiport time domain reflection (TDR) based general deconvolution algorithm. Examples of coupled interconnects and transmission lines are presented to illustrate this technique. / Graduation date: 1997

In the first part, an efficient and reliable a posteriori error estimate is derived for solving three-dimensional static Maxwell's equations based on the lowest order edge elements of the first family. We propose an adaptive finite element method and establish convergence of the adaptive scheme in energy norm under a restriction on the initial mesh size. Any prescribed error tolerance is thus achieved in a finite number of steps. For discretization based on the lowest order edge elements of the second family, a similar adaptive method is designed which guarantees convergence without any initial mesh size restriction. The proofs rely mainly on error and oscillation reduction estimates as well as the Galerkin orthogonality of the edge element approximation. For time-dependent Maxwell's equations, we deduce an efficient and reliable a posteriori error estimate, upon which an adaptive finite element method is built. / In this thesis, we will address three typical problems with discontinuous coefficients in a general Lipschitz polyhedral domain, which are often encountered in numerical simulation of electromagnetism. / The second part deals with a saddle point problem arising from Maxwell's equations. We present an adaptive finite element method on the basis of the lowest order edge elements of the first family and prove its convergence. The main ingredients of the proof are a novel quasi-orthogonality, which replaces the usual Pythagoras relation, which fails in this case, all error reduction depending on an efficient and reliable a posteriori error estimate and an oscillation reduction. We show that this adaptive scheme is a contraction for the sum of some energy error plus the oscillation. Likewise, the above result is generalized to the discretization by the lowest order edge elements of the second family. / We introduce in the third part an adaptive finite element method for solving the eigenvalue problem of the Maxwell system based on an inverse iterative method. By modifying the exact inverse iteration algorithm involving an inner saddle point solver, we construct an adaptive inverse iteration finite element algorithm, which consists of an inexact inner adaptive procedure for a discrete mixed formulation in place of the original saddle point problem. An efficient and reliable a posteriori error estimate is obtained and the convergence of the inner adaptive method is proved. In addition, the important convergence property of the algorithm is studied, which ensures the errors between true solutions (eigenfunction and eigenvalue) and iterative ones to fall below any given tolerance within a finite number of iterations. / Xu, Yifeng. / "June 2007." / Adviser: Jun Zou. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 166-175). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

by Cheng Yat Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 1-6 (2nd gp.)). / Abstracts in English and Chinese. / Acknowledgements / Abstract: / A CD containing the Simulator and Results / List of Figures / List of Tables / Chapter 1. --- Introduction / Introduction --- p.1 / Chapter 2 --- Background Theory / Chapter 2.1 --- Empirical Design Formulas for Some Passive Microwave structures --- p.2 / Chapter 2.2.1 --- Short Dipole and Monopole --- p.4 / Chapter 2.2.2 --- Slot Antenna --- p.6 / Chapter 2.2.3 --- Stripline --- p.8 / Chapter 2.2.4 --- Microstrip --- p.10 / Chapter 2.2 --- Edge Based Finite Element Method and the Generalized Variational Principle --- p.12 / Chapter 2.2.1 --- Vector Finite Element Method for Electromagnetics --- p.14 / Chapter 2.2.1.1 --- Variational Formulation --- p.14 / Chapter 2.2.1.2 --- Advantages in Total Field Formulation --- p.16 / Chapter 2.2.2 --- Formulation by Method of Weighted Residual the Galerkin's Approach --- p.17 / Chapter 2.2.3 --- "the Vector Bases for BRICK, PRISM, TETRA" --- p.21 / Chapter 2.2.3.1 --- BRICK --- p.23 / Chapter 2.2.3.2 --- PRISM --- p.26 / Chapter 2.2.4 --- "Domain Discretization: Mesh Generation Scheme for 3D, 2D, ID Geometrical Entities in the Cartesian Domain" --- p.29 / Chapter 2.3 --- Construction of the Functional with Total Field Formulation --- p.31 / Chapter 2.3.1 --- Vector Wave Equation in the Cartesian Domain --- p.32 / Chapter 2.3.2 --- Boundary Conditions in the Cartesian Domain --- p.33 / Chapter 2.3.2.1 --- Perfect Magnetic Wall (Neumann's Boundary Condition) --- p.34 / Chapter 2.3.2.2 --- Perfect Electric Wall (Dirichlet Boundary Condition) --- p.34 / Chapter 2.3.2.3 --- Anisotropic Perfectly Matched Layer (APML) --- p.35 / Chapter 2.3.2.4 --- 2nd Order Absorbing Boundary Conditions --- p.39 / Chapter 2.3.2.5 --- Plane Wave Incidence (Uinc) --- p.40 / Chapter 2.3.2.6 --- Magnetic Aperture (M) --- p.42 / Chapter 2.3.2.7 --- Passive Lumped Load (ZL1D ) --- p.42 / Chapter 2.3.2.8 --- Current Feed (J) --- p.42 / Chapter 2.3.2.9 --- Voltage Feed (impressed E-field) --- p.43 / Chapter 2.3.2.10 --- Resistive Sheet ( =lst order ABC = standard IBC ) --- p.44 / Chapter 2.4 --- Visualization and Post-Processing of the Solution Field --- p.45 / Chapter 2.4.1 --- Field Pattern Plot --- p.45 / Chapter 2.4.2 --- Impedance at Input Port --- p.45 / Chapter 2.4.3 --- Y-parameter Extraction. --- p.46 / Chapter 3. --- Simulation Results and Discussion; / Chapter 3.1 --- Radiating Structures --- p.48 / Chapter 3.1.1 --- Short Dipole and Monopole --- p.48 / Chapter 3.1.1.1 --- Short Dipole --- p.48 / Chapter 3.1.1.2 --- Equivalent Monopole --- p.50 / Chapter 3.1.2 --- Slot Antenna --- p.52 / Chapter 3.1.2.1 --- Slot Antenna excited by the equivalent magnetic aperture --- p.52 / Chapter 3.1.2.3 --- Slot Antenna Excited by Unit Current Feed with Plane Wave Incidence ( Uinc) --- p.54 / Chapter 3.2 --- Striplines --- p.57 / Chapter 3.2.1 --- A Straight 50Ω Stripline --- p.57 / Chapter 3.2.1.1 --- Optimizing the Thickness and Number of Layer of PML --- p.58 / Chapter 3.2.1.2 --- Different Combination of BRICK and PRISM Mesh --- p.60 / Chapter 3.2.2 --- A Cross Junction --- p.63 / Chapter 3.2.3 --- A Squared 90° Corner --- p.69 / Chapter 3.2.4 --- A Champfered 90° Corner --- p.73 / Chapter 3.2.5 --- A Pair of Slot-Coupled Stripline Each Terminated with Open Circuit at Slot + λ/2 --- p.75 / Chapter 3.2.6 --- A Pair of Slot-Coupled Stripline Each Terminated with Short Circuit at Slot + λ/4 --- p.78 / Chapter 3.2.7 --- A Pair of Slot-Coupled Striplines Each Terminated with Short Circuit at Slot + λ/4 and Shorted through the Slot --- p.80 / Chapter 3.2.8 --- A Pair of Slot-Coupled Striplines Each Terminated with Short Circuit at Slot + λ/4 and has 50Ω Load through the Slot --- p.83 / Chapter 3.3 --- Calculating the Input Impedance ( Vport / Iport ) / Chapter 3.3.1 --- A Pair of Slot-Coupled Stripline Each Terminated with Short Circuit at Slot + λ/4 --- p.85 / Chapter 4 --- Conclusion / Chapter 4.1 --- Conclusion --- p.88 / Chapter 4.2 --- Minor Problems Encountered --- p.89 / Chapter 4.2 --- To Probe Further --- p.90 / Chapter Appendex: --- Implementation of the Edge-Based Finite Element Method / Chapter A.1 --- Mesh Generation Scheme --- p.92 / Chapter A.1.1 --- "Global Node, Edge and Primitive Assignment" --- p.93 / Chapter A.1.2 --- Property Assignment Local to Every Basis and Primitive --- p.94 / Chapter A.2 --- Assembly the Global System of Equations from the Element Stamps of all Primitives wrt. Global Edge Numbering --- p.95 / Chapter A.2.1 --- Setting up the Volumetric Integral for the Vector Wave Equation --- p.95 / Chapter A.2.1.1 --- Volume Integration of Constant Tangential Brick Elements --- p.96 / Chapter A.2.1.2 --- Volume Integration of Constant Tangential Pyramidal Elements --- p.98 / Chapter A.2.2 --- Incorporation of Boundary Conditions --- p.100 / Chapter A.2.2.1 --- Surface Integration of Constant Tangential Brick Elements --- p.100 / Chapter A.2.2.2 --- Surface Integration of Constant Tangential Pyramidal Elements --- p.105 / Chapter A.3 --- Solution to the Final System --- p.110 / Chapter A.3.1 --- Solving a System of Linear Equations by Diagonalization & Blockwise Partitioning --- p.111 / Chapter A.3.2 --- Direct Solution Method for Complex-valued System --- p.114 / Chapter A.4 --- Visualization and Post-Processing of the Solution Field --- p.115 / Chapter A.4.1 --- Field Pattern Visualization --- p.115 / Chapter A.4.2 --- Input Impedance Definition ( Vport /Iport). --- p.115 / Chapter A.4.3 --- Y-parameter Extraction. --- p.115 / Chapter A.4.3.1 --- Surface Integration of Brick Elements --- p.115 / Chapter A.4.3.2 --- Surface Integration of Pyramidal Elements --- p.117 / Chapter A.5 --- Simulation Setup with BRICK+PRISM+higher order TETRA --- p.119 / References / Books: / Journals and Papers: / for Hierarchal Edge Bases and FEM Formulations: / for ABC and PML: / for Mesh Generation: / for Free FEM Source Code Matrix Solver: / Miscellaneous:

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Thesis (MScEng)--University of Stellenbosch, 2002. / ENGLISH ABSTRACT: A computational tool for numerical synthesis via optimization is developed. Only two port waveguide devices are considered. The Finite Element Method (FEM) is used for the electromagnetic analysis. Specifically, the frequency domain electric field FEM is used with vector curl-conforming constant tangential/linear normal brick-shaped elements. Special boundary conditions are used at the ports. These boundary conditions only consider dominant mode propagation. The issues surrounding the implementation of this formulation are discussed. The results generated using this code compare favorably to examples from independent sources. A parametric mesher that is used in conjunction with the FEM is developed. This is done to eliminate the need for human intervention during each iteration of the synthesis procedure. Fast Frequency (FF) techniques are presented to reduce the computational requirements of the synthesis. FF techniques reduce the cost of calculating many frequency samples in a specified band and do not reduce the computational requirements of computing a FEM solution at a single frequency. The FF techniques presented are: Asymptotic Waveform Evaluation (AWE), Model Based Asymptotic Waveform Evaluation (MB-AWE) and Model Based Parameter Estimation (MBPE) . The results obtained using these techniques are compared and the most suitable technique for the synthesizer is selected. MBPE is selected as the most suitable technique for this application. An adaptive sampling algorithm for Model Based Parameter Estimation is presented. The algorithm relies on the difference between multiple models generated from the same samples to determine the sample locations. The use of this algorithm enables a model of a narrow band filter at X-band to be determined using only fourteen FEM solutions. The difference between the model- and the FEM solutions is less then -lOOdBacross the band. A sample synthesis using generalized simulated annealing is presented. A single pole filter in X-band waveguide is successfully synthesized to illustrate the usefulness of the code. The use of FF techniques results in a computational cost saving of a factor of forty times. / AFRIKAANSE OPSOMMING: 'n Rekenaar werktuig vir numeriese sintese deur middel van optimering word ontwikkel. Slegs twee-poort golfleierkomponente word beskou. Die Eindige Element-metode (EEM) word vir die elektromagnetiese analise gebruik. Meer spesifiek, die frekwensiegebied, elektriese-veld EE-formuleering word gebruik, met eurl-ondersteunende, konstant-tagensiaaljlineêr-normaal, baksteenvormige vektorelemente. Spesiale grensvoorwaardes word by die poorte gebruik. Hierdie grensvoorwaardes neem slegs voortplanting van die dominante modus in ag. Die kwessies rondom die implementering van hierdie EEM word bespreek. Resultate wat met hierdie kode verkry word, vergelyk goed met dié vanuit onafhanklike bronne. 'n Parametriese diskretisasie prosedure in ontwikkel, vir gebruik saam met die genoemde EEM, met die doelom menslike interaksie uit die weg te ruim, tydens die sintese proses. Vinnige Frekwensie (VF) tegnieke word beskryf, met die doelom die berekeningskoste van die sintese te verminder. VF tegnieke verminder die berekeningskoste verbonde aan 'n reeks EEM oplosings binne 'n gegewe frekwensieband, maar verminder nie die koste verbonde aan 'n enkel-frekwensie EEM oplossing nie. Die VF tegnieke wat beskryf word, is die volgende: Asimptotiese Golfvorm Evaluasie (AGE), Model Gebaseerder Asimptotiese Golfvormevaluasie (MGAGE) en Model- Gebaseerde Parameterekstraksie (MGPE). Die resultate wat met hierdie metodes verkry word, word vergelyk om sodoende die mees toepaslike VF tegniek te kies. MGPE word gekies as die mees toepaslike tegniek. 'n Aanpasbase monsteringsalgoritme vir MGPE word beskryf. Die algoritme berus op die verskil tussen twee modelle wat vanaf dieselfde stel punte geskep word, om monsterfrekwensiewaardes te bepaal. Die gebruik van hierdie algoritme lei tot 'n model van 'n nou-, X-band filter, vanuit slegs veertien EEM oplossings. Die verskil tussen hierdie model en enige EEM oplossings binne die band, is kleiner as -lOOdB. 'n Voorbeeld sintese, wat gebruik maak van veralgemeende, gesimuleerde versmelting, word beskryf. 'n Enkel-pool filter by X-band word suksesvol gesintetiseer om die bruikbaarheid van die kode te illustreer. 'n Faktor veertig vermindering III berekeningskostes word behaal deur gebruik te maak van VF tegnieke.

The vector finite element method has gained great attention since overcoming the deficiencies incurred by the scalar basis functions for the vector Helmholtz equation. Most implementations of vector FEM have been non-adaptive, where a mesh of the domain is generated entirely in advance and used with a constant degree polynomial basis to assign the degrees of freedom. To reduce the dependency on the users' expertise in analyzing problems with complicated boundary structures and material characteristics, and to speed up the FEM tool, the demand for adaptive FEM grows high. For efficient adaptive FEM, error estimators play an important role in assigning additional degrees of freedom. In this proposal study, hierarchical vector basis functions and four error estimators for p-refinement are investigated for electromagnetic applications.

Various error estimation and adaptive refinement techniques for the solution of electromagnetic integral equations were developed. Residual based error estimators and h-refinement implementations were done for the Method of Moments (MoM) solution of electromagnetic integral equations for a number of different problems. Due to high computational cost associated with the MoM, a cheaper solution technique known as the Locally-Corrected Nyström (LCN) method was explored. Several explicit and implicit techniques for error estimation in the LCN solution of electromagnetic integral equations were proposed and implemented for different geometries to successfully identify high-error regions. A simple p-refinement algorithm was developed and implemented for a number of prototype problems using the proposed estimators. Numerical error was found to significantly reduce in the high-error regions after the refinement. A simple computational cost analysis was also presented for the proposed error estimation schemes. Various cost-accuracy trade-offs and problem-specific limitations of different techniques for error estimation were discussed. Finally, a very important problem of slope-mismatch in the global error rates of the solution and the residual was identified. A few methods to compensate for that mismatch using scale factors based on matrix norms were developed.

Orientador: Cesar José Bonjuani Pagan / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-20T02:16:17Z (GMT). No. of bitstreams: 1 TrindadedeOliveira_Murilo_M.pdf: 8021703 bytes, checksum: 3faa29c4fb8fec84d66f98a7389ed1b5 (MD5) Previous issue date: 2012 / Resumo: Nesta dissertação propomos a análise de uma idealização estabelecida dentro da teoria eletromagnética. A partir de Um Tratado sobre Eletricidade e Magnetismo, James C. Maxwell expõe alguns conceitos físicos relativos ao aterramento elétrico em condutores. Assim, ele estima que a presença de um fio condutor que estabelece a conexão entre um corpo condutor e outro, ou mesmo ao terra elétrico, perturba as características do sistema envolvido (carga, potencial e campo elétrico). Desse modo, Maxwell preconiza que para sistemas teóricos ou idealizados, quão indefinidamente fino seja o fio, indefinidamente menor será a perturbação gerada. A contextualização de uma idealização física dentro do ensino da teoria eletromagnética, especialmente para um curso de engenharia, é necessária no intuito de enfatizar as diferenças entre modelos reais e teóricos, uma vez também que os estudantes destes cursos devem estar interessados no desenvolvimento prático dos conceitos apreendidos em sala de aula. Nesse sentido, quando tratamos do método das imagens, especificamente para o problema de uma carga na presença de um condutor esférico aterrado, temos a oportunidade de explorar os limites de um modelo teórico, delimitando quais nuances podem aproximá-lo de uma aplicação no mundo real. Em vista disso, notamos que a maioria dos livros didáticos usados no ensino do eletromagnetismo, quando lidam com o problema do aterramento da esfera, simplesmente negligenciam a questão suscitada por Maxwell, de modo a transformar o problema em um exercício puramente matemático, sem necessidade de explicar os fundamentos físicos que sustentam a solução do problema. Portanto, o intuito do presente trabalho é desenvolver um modelo cuja solução defina o comportamento físico para ambos os casos (levando em consideração ou não a existência da conexão da esfera com o terra elétrico), bem como verificar os limites deste modelo teórico / Abstract: In this work, we propose the analysis about an idealized established within electromagnetic theory. From A Treatise on Electricity and Magnetism, James C. Maxwell presents some physical concepts related to electrical conductors grounded. In this direction, he estimates that the presence of a straight metallic wire which establishes the connection between a conducting body and another, or even to electrical ground, disturbs the properties of the system involved (charge, potential and electric field). Thus, Maxwell preconize for theoretical or idealized systems, how indefinitely thin is the wire, indefinitely lower is the disturbance created. The context of a physical idealization into the teaching of electromagnetic theory, especially for an engineering degree is required in order to emphasize the differences between real and theoretical models, since the students of these courses should be also interested in the practical development of the concepts learned in the classroom. In this sense, when we discussed the method of images, specifically to the problem of a charge point charge in the presence of a grounded conducting sphere, we have the opportunity to explore the limits of a theoretical model, outlining which nuances can approach it to a real world application. In view of this, we note that most of the textbooks used in teaching electromagnetism, when deals with the problem of grounded sphere, they simply neglect the issue raised by Maxwell. In order to transform the problem into a purely mathematical exercise, without to explain the physical foundations that support the solution of the problem. Therefore, the aim of this work is to develop a model whose solution defines the physical behavior for both cases (taking into account or not the existence of a connection of the sphere with the electrical ground), and to verify the limits of this theoretical model / Mestrado / Eletrônica, Microeletrônica e Optoeletrônica / Mestre em Engenharia Elétrica