We introduce supplemental methods for the finite-difference time-domain (FDTD) analysis of planar multilayered media. The invariance is allowed to be disturbed by any imperfection, provided that these imperfections are local and therefore can be contained within an FDTD simulation grid. We specifically investigate two FDTD methods that were not previously developed for general multilayered media: the near-field-to-far-field transform (NFFFT) and the total-field/scattered-field (TF/SF) boundary (or the plane-wave injector). The NFFFT uses the FDTD output on a virtual surface surrounding the local imperfections and calculates the radiated field. The plane wave injector builds an incident plane wave inside a certain boundary (TF/SF boundary) while allowing any scattered fields created by the imperfections inside the boundary to exit the boundary with complete transparency. The NFFFT is applicable for any lossless multilayered medium, while the plane-wave injector is applicable for any lossy multilayered medium. After developing the respective theories and giving simple examples, we apply the NFFFT and the plane-wave injector to a series of problems. These problems are divided into two main groups. In the first group, we consider plane-wave scattering problems involving perfectly-conducting objects buried in multilayered media. In the second group, we consider problems that involve radiating structures in multilayered media. Specifically, we investigate the reciprocity of antennas radiating in the presence of an ungrounded dielectric slab using the methods developed in this study. Finally, we present our previous work on an entirely different subject, namely, the theoretical analysis of the input admittance of a prolate-spheroidal monopole fed by a coaxial line through a ground plane.

The Method of Moments (MoM) has been widely used for the full-wave electromagnetic analysis of planar multilayered media. However, the MoM is a computationally intensive process and requires considerable computer resources to perform the analysis. Thus, several efficient numerical techniques both in the spectral domain and spatial domain are investigated and further developed in this research. Two fitting procedures, i.e., the Rational Function Fitting Method (RFFM) and the Discrete Complex Image Method (DCIM), are investigated and developed in order to obtain closed-form spatial-domain Green's functions (GFs). Because the subtraction of the surface-wave pole contribution plays an important role for the accurate estimation of the spatial-domain GFs via DCIM, an efficient and accurate surface-wave pole location method is developed to find all the surface-wave poles for general multilayered media. The RFFM can be realized through either the Total Least Square Algorithm (TLSA) or the Vector Fitting (VECTFIT) method. Both the RFFM using VECTFIT and DCIM are detailed in step by step procedures. An efficient and low cost algorithm combining the advantages of DCIM and TLSA is also developed to evaluate the closed-form Green's functions for general multilayered media. A prototype version of the Full-Wave Layered-Interconnect Simulator (UA-FWLIS) was developed by analytically calculating the MoM reaction elements via Cauchy's residue theorem and the Complementary Incomplete Lipschitz-Hankel Integrals in stripline structures. After applying RFFM via VECTFIT to the G-functions, which are directly related to the spectral-domain GFs for microstrip structures, a procedure that is similar to the one used in the previously developed UA-FWLIS for stripline structures can be applied to calculate the MoM reaction elements analytically when the two reaction cells are close (< 0.1λ₀) in the spectral domain via the Electrical Field Integral Equation (EFIE). When the two reaction cells are far enough away (> 0.10.1λ₀), a simple expression for the reaction element can be obtained in the spatial domain via the Mixed Potential Integral Equation (MPIE) by a summation of a few complex image terms for the evaluation of the vector and scalar GFs. An efficient hybrid spectral-spatial method is thus developed to extend UA-FWLIS to microstrip structures. The method is validated by several numerical examples.

[pt] Esta tese apresenta um estudo sobre técnicas de modelagem numérica utilizadas na análise da propagação eletromagnética em formações geofísicas comumente encontradas na perfuração de poços de petróleo. O emprego de sensores eletromagnéticos adjacentes à broca de perfuração permite a inferência dos parâmetros constitutivos do solo ao redor do poço. Nos últimos anos, os avanços da tecnologia de perfilagem eletromagnética permitiram a modelagem em tempo real do problema, possibilitando direcionar a perfuração do poço a fim de maximizar a exploração de petróleo, gás, e outros hidrocarbonetos fósseis. Formações geofísicas complexas são predominantes neste tipo de problema, e geralmente são modeladas usando técnicas numéricas de força bruta como os métodos de diferenças finitas, dos elementos finitos ou dos volumes finitos. No entanto, estas técnicas têm um custo computacional relativamente alto em termos de memória e tempo de processamento. O avanço da tecnologia de perfilagem em tempo real requer abordagens mais eficientes. Neste trabalho nós empregamos o método do casamento de modos combinado com uma série de características positivas dos métodos pseudoanalíticos conhecidos na literatura para obter uma técnica inédita que permite analisar poços direcionais com estratificações radiais e longitudinais em formações geofísicas anisotrópicas. A técnica proposta permite modelar problemas ainda não explorados, mas com motivação tecnológica iminente, como a propagação eletromagnética ao longo de poços curvados e a perfuração em camadas inclinadas em relação ao eixo axial do poço. Nós apresentamos uma série de resultados de validação que demonstram que a técnica introduzida neste trabalho pode modelar de forma acurada e eficiente sensores de perfilagem eletromagnética usados na exploração de petróleo e gás. / [en] This research presents a study on numerical techniques to model the electromagnetic propagation in geophysical formations commonly encountered in oil well drilling. The employment of electromagnetic sensors surrounding the drill bit allows inferring the constitutive parameters of the soil around the well. In recent years, advances in electromagnetic logging technology have enabled the real-time modeling of this problem. In this way, the drilling direction can be guided in order to maximize the exploitation of oil, gas, and other fossil hydrocarbons. The complex geophysical formations that are prevalent in this type of problem can be effectively handled using brute-force numerical techniques such as finite-differences, finite-elements and finite-volumes. However, these techniques suffer from relatively high cost in terms of both computer memory and CPU time. The advancement of real-time logging technology demands approaches that are more efficient than purely numerical methods. In this work, we employ the mode-matching technique combining attractive features of the well-known pseudo-analytical approaches to obtain a new technique for analyzing directional well-logging tools in anisotropic formations with both radial and axial stratifications. The proposed technique allows to model problems not yet explored, but with a strong technological motivation, such as electromagnetic propagation along curved wells and drilling along inclined layers. We present a series of validation results showing that the novel technique introduced in this study can model accurately and efficiently electromagnetic logging sensors used in oil and gas exploration.

The employment of real time NDT systems has been spread widely last years. It is very important to control in real-time layer thicknesses of multi-layered materials during manufacturing process. In this work multi-layer thickness measurement digital signal processing methods are evaluated. Presented real-time nondestructive testing system and signal propagation model is a background for measurement algorithm analysis and development. In this work multi-layer thickness measurement problem is addressed with a different approach, by applying correlation functions on parts of the ultrasonic signal, thus reducing the overall computational complexity.

[pt] Muitos dispositivos e estruturas empregados para guiar ondas eletromagnéticas apresentam conformidade cilíndrica. Aplicações sensíveis de engenharia de micro-ondas e de dispositivos ópticos integrados empregam, muitas vezes, materiais não homogêneos, anisotrópicos e dissipativos, de modo que a pesquisa por modelos computacionais robustos e acurados é um tópico de notável interesse para a Engenharia Elétrica. Este trabalho apresenta uma técnica semianalítica para resolver problemas de valor de contorno associados a guias de onda cilíndricos, anisotrópicos e não homogêneos. Nossa metodologia permite modelar estruturas com camadas radiais, com anisotropia uniaxial, e com perdas. A solução proposta parte das equações de Maxwell para campos harmônicos no tempo, e emprega uma expansão modal em termos da série de Bessel-Fourier. Os autovalores associados ao problema são obtidos por meio do método do winding number, em que diversas abordagens para o cálculo das integrais de caminho no plano complexo são exploradas. Para analisar junções entre guias de ondas estratificados, empregamos a técnica de casamento de modos baseada na conservação da Reação dos campos. Nossa formulação é capaz de avaliar os efeitos da excitação e do acoplamento entre modos puros (TM, TE, e TEM) em guias de ondas homogêneos, bem como dos modos híbridos em estruturas complexas. Uma série de resultados numéricos são apresentados e mostram a capacidade da metodologia desenvolvida nesta pesquisa para caracterizar corretamente estruturas cilíndricas compostas por meios complexos (não homogêneos, anisotrópicos e dissipativos) de forma robusta e computacionalmente eficiente se comparado com outras técnicas convencionais de eletromagnetismo computacional. / [en] Many devices and structures used to guide electromagnetic waves are conformal with the cylindrical coordinates. Sensitive applications of microwave engineering and integrated optical devices often use non-homogeneous, anisotropic and dissipative materials, so that the research for robust and accurate computational models is a topic of remarkable interest for Electrical Engineering. This work presents a semi-analytical technique for solving boundary-value problems associated with cylindrical, anisotropic, and non-homogeneous waveguides. Our methodology allows us to model structures with radial layers, with uniaxial anisotropy, and with losses. The proposed solution starts from Maxwell s equations for time-harmonic electromagnetic fields and employs a modal expansion in terms of the Bessel-Fourier series. The eigenvalues associated with the problem are obtained using the winding number method, in which several approaches for calculating complex-plane contour integrals are explored in detail. In order to properly analyze the junctions between sections of stratified waveguides, we employ a mode-matching technique based on the conservation of the Reaction of the fields. Our formulation can handle the effects of excitation and coupling between pure modes (TM, TE, and TEM) in homogeneous waveguides, as well as hybrid modes in complex structures. A series of numerical results are presented and show the capacity of the methodology developed here to correctly characterize cylindrical structures composed of complex media (inhomogeneous, anisotropic, and dissipative) in a robust and computationally-efficient fashion if compared to other conventional computational electromagnetic techniques.