Ground-Penetrating Radar (GPR) is a non-destructive electromagnetic investigative tool used in many applications across the fields of engineering and geophysics. The propagation of electromagnetic waves in lossy materials is complex and over the past 20 years, the computational modelling of GPR has developed to improve our understanding of this phenomenon. This research focuses on the development of accurate numerical models of widely-used, high-frequency commercial GPR antennas. High-frequency, highresolution GPR antennas are mainly used in civil engineering for the evaluation of structural features in concrete i. e., the location of rebars, conduits, voids and cracking. These types of target are typically located close to the surface and their responses can be coupled with the direct wave of the antenna. Most numerical simulations of GPR only include a simple excitation model, such as an infinitesimal dipole, which does not represent the actual antenna. By omitting the real antenna from the model, simulations cannot accurately replicate the amplitudes and waveshapes of real GPR responses. Numerical models of a 1.5 GHz Geophysical Survey Systems, Inc. (GSSI) antenna and a 1.2 GHz MALÅ GeoScience (MALÅ) antenna have been developed. The geometry of antennas is often complex with many fine features that must be captured in the numerical models. To visualise this level of detail in 3d, software was developed to link Paraview—an open source visualisation application which uses the Visualisation Toolkit (VTK)—with GprMax3D—electromagnetic simulation software based on the Finite-Difference Time-Domain (FDTD) method. Certain component values from the real antennas that were required for the models could not be readily determined due to commercial sensitivity. Values for these unknown parameters were found by implementing an optimisation technique known as Taguchi’s method. The metric used to initially assess the accuracy of the antenna models was a cross-corellation of the crosstalk responses from the models with the crosstalk responses measured from the real antennas. A 98 % match between modelled and real crosstalk responses was achieved. Further validation of the antenna models was undertaken using a series of laboratory experiments where oil-in-water (O/W) emulsions were created to simulate the electrical properties of real materials. The emulsions provided homogeneous liquids with controllable permittivity and conductivity and enabled different types of targets, typically encountered with GPR, to be tested. The laboratory setup was replicated in simulations which included the antenna models and an excellent agreement was shown between the measured and modelled data. The models reproduced both the amplitude and waveshape of the real responses whilst B-scans showed that the models were also accurately capturing effects, such as masking, present in the real data. It was shown that to achieve this accuracy, the real permittivity and conductivity profiles of materials must be correctly modelled. The validated antenna models were then used to investigate the radiation dynamics of GPR antennas. It was found that the shape and directivity of theoretically predicted far-field radiation patterns differ significantly from real antenna patterns. Being able to understand and visualise in 3d the antenna patterns of real GPR antennas, over realistic materials containing typical targets, is extremely important for antenna design and also from a practical user perspective.

Theoretical and experimental plasmonics is a growing field as a method to create near fields at sub-wavelength distances. In this thesis, a finite-difference time-domain method is used to simulate electromagnetic waves onto a thin film that present of nickel nanorods with sharp apexes. The absorbed, transmitted, and reflected fields were shown to depend linearly on silver film thickness and nanotip length. The electric field is visualized along the tip to show strong charge density along the base of the tip’s apex and how that density changes for wavelength, metal, and source tilt. Lastly, the study shows gold film on the nanotip apex provides the largest enhancement of the electric field for the wavelengths 532, 572, and 633 nm.

<div>Multiscale and multiphysics have been two major challenges in analyzing and designing new emerging engineering devices, materials, circuits, and systems. When simulating a multiscale problem, numerical methods have to overcome the challenges in both space and time to account for the scales spanning many orders of magnitude difference. In the finite-difference time-domain (FDTD) method, subgridding techniques have been developed to address the multiscale challenge. However, the accuracy and stability in existing subgridding algorithms have always been two competing factors. In terms of the analysis of a multiphysics problem, it involves the solution of multiple partial differential equations. Existing partial differential equation solvers require solving a system matrix when handling inhomogeneous materials and irregular geometries discretized into unstructured meshes. When the problem size, and hence the matrix size, is large, existing methods become highly inefficient.</div><div><br></div><div>In this work, a symmetric positive semi-definite FDTD subgridding algorithm in both space and time is developed for fast transient simulations of multiscale problems. This algorithm is stable and accurate by construction. Moreover, the method is further made unconditionally stable, by analytically finding unstable modes, and subsequently deducting them from the system matrix. To address the multiphysics simulation challenge, we develop a matrix-free time domain method for solving thermal diffusion equation, and the combined Maxwell-thermal equations, in arbitrary unstructured meshes. The counterpart of the method in frequency domain is also developed for fast frequency-domain analysis. In addition, a generic time marching scheme is proposed for simulating unsymmetrical systems to guarantee their stability in time domain. </div>

The Finite Difference Time Domain (FDTD) Method has been a powerful tool in numerical simulation of electromagnetic (EM) problems for decades. In recent years, it has also been applied to biomedical research to investigate the interaction between EM waves and biological tissues. In Wireless Body Area Networks (WBANs) studies, to better understand the localization problem within the body, an accurate source/receiver model must be investigated. However, the traditional source models in FDTD involve effective volume and may cause error in near field arbitrary direction. This thesis reviews the basic mathematical and numerical foundation of the Finite Difference Time Domain method and the material properties needed when modeling a human body in FDTD. Then Coincident Phase Centers (CPCs) point sources models have been introduced which provide nearly the same accuracy at the distances as small as 3 unit cells from the phase center. Simultaneously, this model outperforms the usual sources in the near field when an arbitrary direction of the electric or magnetic dipole moment is required.

This work considers the synthesis of brass instrument sounds using time-domain numerical methods. The operation of such a brass instrument is as follows. The player's lips are set into motion by forcing air through them, which in turn creates a pressure disturbance in the instrument mouthpiece. These disturbances produce waves that propagate along the air column, here described using one spatial dimension, to set up a series of resonances that interact with the vibrating lips of the player. Accurate description of these resonances requires the inclusion of attenuation of the wave during propagation, due to the boundary layer effects in the tube, along with how sound radiates from the instrument. A musically interesting instrument must also be flexible in the control of the available resonances, achieved, for example, by the manipulation of valves in trumpet-like instruments. These features are incorporated into a synthesis framework that allows the user to design and play a virtual instrument. This is all achieved using the finite-difference time-domain method. Robustness of simulations is vital, so a global energy measure is employed, where possible, to ensure numerical stability of the algorithms. A new passive model of viscothermal losses is proposed using tools from electrical network theory. An embedded system is also presented that couples a one-dimensional tube to the three-dimensional wave equation to model sound radiation. Additional control of the instrument using a simple lip model as well a time varying valve model to modify the instrument resonances is presented and the range of the virtual instrument is explored. Looking towards extensions of this tool, three nonlinear propagation models are compared, and differences related to distortion and response to changing bore profiles are highlighted. A preliminary experimental investigation into the effects of partially open valve configurations is also performed.

Les travaux effectués durant cette thèse s’inscrivent dans le cadre d’une collaboration entre l’équipe CEM de l’Institut Pascal et l’équipe EDPAN du Laboratoire de Mathématiques de l’Université Blaise Pascal de Clermont-Ferrand. Nous présentons ici une étude qui, partant de l’analyse du processus de Retournement Temporel en électromagnétisme, a débouché sur le développement d’une méthode originale baptisée Linear Combination of Configuration Fields (LCCF) ou, en français, Combinaison Linéaire de Configurations de Champs. Après avoir introduit l’ensemble des outils et méthodes utilisés dans ces travaux, ce mémoire détaille le processus de Retournement Temporel de base ainsi qu’un ajout apporté à celui-ci. Par la suite, la méthode LCCF s’étant révélée applicable à plusieurs problèmes d’identification de sources en électromagnétisme, nous nous consacrons à la présentation détaillée des différentes variantes de celle-ci et nous illustrons son utilisation sur de nombreux exemples numériques. / This Ph.D thesis is the result of a collaboration between the CEM team of Pascal Institute and the EDPAN team of the Laboratory of Mathematics of the Blaise Pascal University in Clermont-Ferrand. We present here a study based on Time Reversal process in Electromagnetics. This work led to the development of a novel method called Linear Combination of Configuration Field (LCCF). This thesis first introduces the tools and the numerical methods used during this work. Then, we describe the Time Reversal process and a possible improvement to the basic technic. Afterwards, several possible applications of the LCCF method to electromagnetic source identification problems are detailed and we illustrate each of it on various numerical examples.

Cette thèse constitue un ensemble de travaux et de réflexions sur la question de la modélisation des applications électromagnétiques en nano-optique en utilisant la méthode des différences finies dans le domaine temporel (FDTD). Dans un premier temps, des codes FDTD bidimentionnels pour le calcul de bandes interdites photoniques ont été mis en oeuvre. Ces algorithmes tiennent comptes de la dispersion des métaux nobles dans la gamme optique décrite par le modèle de Drude ou de Drude-Lorentz. Ces programmes FDTD permettent de tenir compte de la propagation soit dans le plan perpendiculaire au plan d'invariance (appelé "cas dans le plan" ou "in-plane" en anglais) pour les deux polarisations TE et TM ainsi que le cas d'une propagation quelconque hors du plan (ou off-plane). Plusieurs diagrammes de bandes sont calculés et présentés pour les structures carrées et triangulaires dans les cas diélectriques et métalliques. Ensuite, nous avons implémenté un code BOR-FDTD, basé sur la discrétisation des équations de Maxwell exprimées en coordonnées cylindriques, pour la modélisation des guides d'ondes (ou d'autres objets) à symétrie de révolution. Les conditions absorbantes PML pour décrire l'espace libre sont intégrées à la BOR-FDTD ainsi que les deux modèles de Drude et de Drude-Lorentz. Des simulations ont été effectuées pour le calcul de modes propres de guides d'ondes coaxiaux et cylindriques sub-longueurs d'ondes faits en métal parfait et en métal réel (argent par exemple). Les résultats montrent la possibilité de guider des signaux optiques sans beaucoup de pertes dans un guide coaxial fait en argent de dimensions sublongueur d'onde. Ce dernier résultat est original et constitue une très importante avancée dans le domaine de la "nanoconnectique" en optique, plus particulièrement pour l'optique intégrée. Puis, un autre code numérique FDTD-3D a été élaboré pour la modélisation des structures périodiques (type cristaux photoniques tridimensionnels) éclairées en incidence oblique. Ce code intègre aussi les couches absorbantes PML ainsi que les modèles de dispersion de Drude et de Drude-lorentz. Les résultats obtenus sont comparés à ceux issus d'autres modèles théoriques. Les applications de ce code à l'étude de radôme, à l'excitation du mode TEM de la structure métallique à ouvertures annulaires et aux calculs des spectres d'extinction Raman montrent l'efficacité de la FDTD pour la modélisation de telles structures.

Simulating wave propagation in microstrip lines with Gyrotropic magnetic substrate is considered in this thesis. Since the static internal field distribution has an important effect on the device behavior, accurate determination of the internal fields are considered as well. To avoid the losses at microwave frequencies it is assumed that the magnetic substrate is saturated in the direction of local internal field. An iterative method to obtain the magnetization distribution has been developed. It is applied to a variety of nonlinear nonuniform magnetic material configurations that one may encounter in the design stage, subject to a nonuniform applied field. One of the main characteristics of the proposed iterative method to obtain the static internal field is that the results are supported by a uniqueness theorem in magnetostatics. The series of solutions Mn,Hn, where n is the iteration number, minimize the free Gibbs energy G(M) in sequence. They also satisfy the constitutive equation M = χH at the end of each iteration better than the previous one. Therefore based on the given uniqueness theorem, the unique stable equilibrium state M is determined. To simulate wave propagation in the Gyrotropic magnetic media a new FDTD formulation is proposed. The proposed formulation considers the static part of the electromagnetic field, obtained by using the iterative approach, as parameters and updates the dynamic parts in time. It solves the Landau-Lifshitz-Gilbert equation in consistency with Maxwell’s equations in time domain. The stability of the initial static field distribution ensures that the superposition of the time varying parts due to the propagating wave will not destabilize the code. Resonances in a cavity filled with YIG are obtained. Wave propagation through a microstrip line with YIG substrate is simulated. Magnetization oscillations around local internal field are visualized. It is proved that the excitation of magnetization precession which is accompanied by the excitation of magnetostatic waves is responsible for the gap in the scattering parameter S12. Key characteristics of the wide microstrip lines are verified in a full wave FDTD simulation. These characteristics are utilized in a variety of nonreciprocal devices like edgemode isolators and phase shifters.

Simulating wave propagation in microstrip lines with Gyrotropic magnetic substrate is considered in this thesis. Since the static internal field distribution has an important effect on the device behavior, accurate determination of the internal fields are considered as well. To avoid the losses at microwave frequencies it is assumed that the magnetic substrate is saturated in the direction of local internal field. An iterative method to obtain the magnetization distribution has been developed. It is applied to a variety of nonlinear nonuniform magnetic material configurations that one may encounter in the design stage, subject to a nonuniform applied field. One of the main characteristics of the proposed iterative method to obtain the static internal field is that the results are supported by a uniqueness theorem in magnetostatics. The series of solutions Mn,Hn, where n is the iteration number, minimize the free Gibbs energy G(M) in sequence. They also satisfy the constitutive equation M = χH at the end of each iteration better than the previous one. Therefore based on the given uniqueness theorem, the unique stable equilibrium state M is determined. To simulate wave propagation in the Gyrotropic magnetic media a new FDTD formulation is proposed. The proposed formulation considers the static part of the electromagnetic field, obtained by using the iterative approach, as parameters and updates the dynamic parts in time. It solves the Landau-Lifshitz-Gilbert equation in consistency with Maxwell’s equations in time domain. The stability of the initial static field distribution ensures that the superposition of the time varying parts due to the propagating wave will not destabilize the code. Resonances in a cavity filled with YIG are obtained. Wave propagation through a microstrip line with YIG substrate is simulated. Magnetization oscillations around local internal field are visualized. It is proved that the excitation of magnetization precession which is accompanied by the excitation of magnetostatic waves is responsible for the gap in the scattering parameter S12. Key characteristics of the wide microstrip lines are verified in a full wave FDTD simulation. These characteristics are utilized in a variety of nonreciprocal devices like edgemode isolators and phase shifters.

With the trends of fast edge rates, high clock frequencies, and low voltage levels for the high-speed digital computer systems, the ground bounce noise (GBN) or simultaneously switching noise (SSN) on the power/ground planes is becoming one of the major challenges for designing the high-speed circuits. In order to analyze the impact of the GBN on signal integrity (SI) and electromagnetic interference (EMI), an accurate and efficient modeling approach that considers the active devices and passive interconnects is required. This thesis focuses on two points. One is developing modeling approaches for analyzing the GBN effects, and the other is proposing solutions to reduce it. First, based on the FDTD algorithm several efficient modeling approaches including equivalent current-source method (ECSM), Kirchoff surface integral representation (KSIR), and slot-corrected 2D-FDTD are developed. After that, a power/ground-planes design for efficiently eliminating the GBN in high-speed digital circuits is proposed by using low-period coplanar electromagnetic bandgap (LPC-EBG) structure. Its extinctive behaviors of low radiation and broadband suppression of the GBN is demonstrated numerically and experimentally. Good agreements are seen.