Bending loss in silicon-on-insulator rib waveguides was calculated using conformal mapping of the curved waveguide to an equivalent straight waveguide. Finite-element analysis with perfectly matched layer boundaries was used to solve the vector wave equation. Transmission loss was experimentally measured as a function of bend radius for several SOI waveguides. Good agreement was found between simulated and measured losses, and this technique was confirmed as a good predictor for loss and for minimum bend radius for efficient design.

The main objective of this research is to model and analyse complex electromagnetic problems by means of a new hybridised computational technique combining the frequency domain Method of Moments (MoM), Finite-Difference Time-Domain (FDTD) method and a subgridded Finite-Difference Time-Domain (SGFDTD) method. This facilitates a significant advance in the ability to predict electromagnetic absorption in inhomogeneous, anisotropic and lossy dielectric materials irradiated by geometrically intricate sources. The Method of Moments modelling employed a two-dimensional electric surface patch integral formulation solved by independent linear basis function methods in the circumferential and axial directions of the antenna wires. A similar orthogonal basis function is used on the end surface and appropriate attachments with the wire surface are employed to satisfy the requirements of current continuity. The surface current distributions on structures which may include closely spaced parallel wires, such as dipoles, loops and helical antennas are computed. The results are found to be stable and showed good agreement with less comprehensive earlier work by others. The work also investigated the interaction between overhead high voltage transmission lines and underground utility pipelines using the FDTD technique for the whole structure, combined with a subgridding method at points of interest, particularly the pipeline. The induced fields above the pipeline are investigated and analysed. FDTD is based on the solution of Maxwell's equations in differential form. It is very useful for modelling complex, inhomogeneous structures. Problems arise when open-region geometries are modelled. However, the Perfectly Matched Layer (PML) concept has been employed to circumvent this difficulty. The establishment of edge elements has greatly improved the performance of this method and the computational burden due to huge numbers of time steps, in the order of tens of millions, has been eased to tens of thousands by employing quasi-static methods. This thesis also illustrates the principle of the equivalent surface boundary employed close to the antenna for MoM-FDTD-SGFDTD hybridisation. It depicts the advantage of using hybrid techniques due to their ability to analyse a system of multiple discrete regions by employing the principle of equivalent sources to excite the coupling surfaces. The method has been applied for modelling human body interaction with a short range RFID antenna to investigate and analyse the near field and far field radiation pattern for which the cumulative distribution function of antenna radiation efficiency is presented. The field distributions of the simulated structures show reasonable and stable results at 900 MHz. This method facilitates deeper investigation of the phenomena in the interaction between electromagnetic fields and human tissues.

Dans cette thèse, nous étudions la convergence de méthode de type éléments finis pour les équations de Maxwell en régime harmonique avec condition au bord d'impédance et l'équation de Helmholtz avec une couche parfaitement absorbante(PML). On étudie en premier, la formulation régularisée de l'équation de Maxwell en régime harmonique avec condition au bord d'impédance (qui consiste à ajouter le term ∇ div à l'équation originale pour avoir un problème elliptique) et on garde la condition d'impédance comme une condition au bord essentielle. Pour des domaines à bord régulier, le caractère bien posé de cette formulation est bien connu mais cela n'est pas le cas pour des domaines polyédraux convexes. On commence alors le premier chapitre par la preuve du caractère bien posé dans le cas du polyèdre convexe, qui est basé sur le fait que l'espace variationnel est inclus dans H¹. Dans le but d'avoir des estimations explicites en le nombre d'onde k de ce problème, il est obligatoire d'avoir des résultats de stabilité explicites en ce nombre d'onde. C'est aussi proposé, pour quelques situations particulières, dans ce chapitre. Dans le second chapitre on décrit les singularités d'arêtes et de coins pour notre problème. On peut alors déduire la régularité de la solution du problème original, ainsi que de son adjoint. On a tous les ingrédients pour proposer une analyse de convergence explicite en k pour une méthode d'éléments finis avec éléments de Lagrange. Dans le troisième chapitre, on considère une méthode d'éléments finis hp non conforme pour un domaine à bord régulier. Pour obtenir des estimations explicites en k, on introduit un résultat de décomposition, qui sépare la solution du problème original (ou de son adjoint) en une partie régulière mais fortement oscillante et une partie moins régulière mais peu oscillante. Ce résultat permet de montrer des estimations explicites en k. Le dernier chapitre est dédié à l'équation de Helmholtz avec une PML. L'équation de Helmholtz dans l'espace entier est souvent utilisée pour modéliser la diffraction d'onde acoustique (en régime harmonique), avec la condition de radiation à l'infini de Sommerfeld. L'ajout d'une PML est une façon pour passer d'un domaine infini à un domaine fini, elle correspond à l'ajout d'une couche autour du domaine de calcul qui absorbe très vite toutes les ondes sortantes. On propose en premier un résultat de stabilité explicite en k. On propose alors deux schémas numériques, une méthode d'éléments finis hp et une méthode multi- échelle basée sur un sous-espace local de correction. Le résultat de stabilité est utilisé pour mettre en relation de choix des paramètres des méthodes numériques considérées avec k. Nous montrons aussi des estimations d'erreur a priori. A la fin de ces chapitres, des tests numériques sont proposés pour confirmer nos résultats théoriques. / In this thesis, we propose wavenumber explicit convergence analyses of some finite element methods for time-harmonic Maxwell's equations with impedance boundary condition and for the Helmholtz equation with Perfectly Matched Layer (PML). We first study the regularized formulation of time-harmonic Maxwell's equations with impedance boundary conditions (where we add a ∇ div-term to the original equation to have an elliptic problem) and keep the impedance boundary condition as an essential boundary condition. For a smooth domain, the wellposedness of this formulation is well-known. But the well-posedness for convex polyhedral domain has been not yet investigated. Hence, we start the first chapter with the proof of the well-posedness in this case, which is based on the fact that the variational space is embedded in H¹. In order to perform a wavenumber explicit error analysis of our problem, a wavenumber explicit stability estimate is mandatory. We then prove such an estimate for some particular configurations. In the second chapter, we describe the corner and edge singularities for such problem. Then we deduce the regularity of the solution of the original and the adjoint problem, thus we have all ingredients to propose a explicit wavenumber convergence analysis for h-FEM with Lagrange element. In the third chapter, we consider a non conforming hp-finite element approximation for domains with a smooth boundary. To perform a wavenumber explicit error analysis, we split the solution of the original problem (or its adjoint) into a regular but oscillating part and a rough component that behaves nicely for large frequencies. This result allows to prove convergence analysis for our FEM, again explicit in the wavenumber. The last chapter is dedicated to the Helmholtz equation with PML. The Helmholtz equation in full space is often used to model time harmonic acoustic scattering problems, with Sommerfeld radiation condition at infinity. Adding a PML is a way to reduce the infinite domain to a finite one. It corresponds to add an artificial absorbing layer surrounding a computational domain, in which scattered wave will decrease very quickly. We first propose a wavenumber explicit stability result for such problem. Then, we propose two numerical discretizations: an hp-FEM and a multiscale method based on local subspace correction. The stability result is used to relate the choice of the parameters in the numerical methods to the wavenumber. A priori error estimates are shown. At the end of each chapter, we perform numerical tests to confirm our theoritical results.

We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil's response to probing elastic waves. We use the complete waveforms of the medium's response to drive the inverse problem. Specifically, we use a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lame parameters. We discuss strategies that lend algorithmic robustness to the proposed inversion schemes. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). The PML is a buffer zone that surrounds the domain of interest, and enforces the decay of outgoing waves. In order to resolve the forward problem, we present a hybrid finite element approach, where a displacement-stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. We discuss several time-integration schemes, including an explicit Runge-Kutta scheme, which is well-suited for large-scale problems on parallel computers. We report numerical results demonstrating stability and efficacy of the forward wave solver, and also provide examples attesting to the successful reconstruction of the two Lame parameters for both smooth and sharp profiles, using synthetic records. We also report the details of two field experiments, whose records we subsequently used to drive the developed inversion algorithms in order to characterize the sites where the field experiments took place. We contrast the full-waveform-based inverted site profile against a profile obtained using the Spectral-Analysis-of-Surface-Waves (SASW) method, in an attempt to compare our methodology against a widely used concurrent inversion approach. We also compare the inverted profiles, at select locations, with the results of independently performed, invasive, Cone Penetrometer Tests (CPTs). Overall, whether exercised by synthetic or by physical data, the full-waveform inversion method we discuss herein appears quite promising for the robust subsurface imaging of near-surface deposits in support of geotechnical site characterization investigations.

The main objective of this research is to model and analyse complex electromagnetic problems by means of a new hybridised computational technique combining the frequency domain Method of Moments (MoM), Finite-Difference Time-Domain (FDTD) method and a subgridded Finite-Difference Time-Domain (SGFDTD) method. This facilitates a significant advance in the ability to predict electromagnetic absorption in inhomogeneous, anisotropic and lossy dielectric materials irradiated by geometrically intricate sources. The Method of Moments modelling employed a two-dimensional electric surface patch integral formulation solved by independent linear basis function methods in the circumferential and axial directions of the antenna wires. A similar orthogonal basis function is used on the end surface and appropriate attachments with the wire surface are employed to satisfy the requirements of current continuity. The surface current distributions on structures which may include closely spaced parallel wires, such as dipoles, loops and helical antennas are computed. The results are found to be stable and showed good agreement with less comprehensive earlier work by others. The work also investigated the interaction between overhead high voltage transmission lines and underground utility pipelines using the FDTD technique for the whole structure, combined with a subgridding method at points of interest, particularly the pipeline. The induced fields above the pipeline are investigated and analysed. FDTD is based on the solution of Maxwell¿s equations in differential form. It is very useful for modelling complex, inhomogeneous structures. Problems arise when open-region geometries are modelled. However, the Perfectly Matched Layer (PML) concept has been employed to circumvent this difficulty. The establishment of edge elements has greatly improved the performance of this method and the computational burden due to huge numbers of time steps, in the order of tens of millions, has been eased to tens of thousands by employing quasi-static methods. This thesis also illustrates the principle of the equivalent surface boundary employed close to the antenna for MoM-FDTD-SGFDTD hybridisation. It depicts the advantage of using hybrid techniques due to their ability to analyse a system of multiple discrete regions by employing the principle of equivalent sources to excite the coupling surfaces. The method has been applied for modelling human body interaction with a short range RFID antenna to investigate and analyse the near field and far field radiation pattern for which the cumulative distribution function of antenna radiation efficiency is presented. The field distributions of the simulated structures show reasonable and stable results at 900 MHz. This method facilitates deeper investigation of the phenomena in the interaction between electromagnetic fields and human tissues. / Ministry of Higher Education Malaysia and Universiti Tun Hussein Onn Malaysia (UTHM)

L’accélération par sillage laser (ASL) repose sur l’interaction entre un faisceau laser intense et un plasma sous-dense. Au travers de cette interaction, une onde de plasma est générée avec un fort champ accélérateur, de trois ordres de grandeur plus élevé que celui d’un accélérateur conventionnel, rendant envisageable la réalisation d’accélérateurs futurs plus compacts. Pour la conception d’un futur accélérateur, un faisceau d’électrons de forte charge, faible dispersion en énergie et faible émittance doit être accéléré à des grandes énergies. Pour ce faire, la solution consiste à accélérer ces électrons dans un schéma multi-étages, qui est composé de trois étages: un injecteur, une ligne de transport et un accélérateur. Ce travail de thèse porte sur la modélisation de l’injecteur avec le code PIC Warp et sur les méthodes numériques telles que la technique de Lorentz-boosted frame pour diminuer le temps de calcul et la couche absorbante parfaite de Bérenger (PML) pour assurer la précision des calculs numériques. Ce travail de thèse a démontré l’efficacité de la PML dans les schémas FDTD à des ordres élevés et pseudo-spectral. Il a aussi démontré la convergence des résultats des simulations réalisées avec la technique de Lorentz-boosted frame dans un régime fortement non-linéaire de l’injecteur, permettant d’accélérer les calculs d’un facteur important (36) tout en assurant leur précision. La modélisation effectuée dans cette thèse a permis d’analyser et de comprendre les résultats expérimentaux, ainsi que de prédire les résultats des futures expériences. Plusieurs méthodes d’optimisation de l’injecteur ont également été proposées pour la génération d’un faisceau d’électrons conforme aux spécifications d’un futur accélérateur. / Laser Wakefield Acceleration (LWFA) relies on the interaction between an intense laser pulse and an under-dense plasma. This interaction generates a plasma wave with a strong accelerating field, which is three orders of magnitude higher than the one of the conventional accelerator; more compact accelerator is therefore theoretically possible. In the design of a future accelerator, a high quality electron bunch with a high charge, low energy spread and low emittance has to be accelerated to high energies. A solution for this is a multi-stage accelerator, which consists of an injector, a transport line and accelerator stages. This research work focuses on the modelling of the injector using the PIC code Warp and on the numerical methods such as the Lorentz-boosted frameto speedup calculations and the Perfectly Matched Layer (PML) to ensure the precision in numerical calculations. The outcome of this thesis has demonstrated the efficiency of the PML in the high-order FDTD and the pseudo-spectral solvers. Besides, it has also demonstrated the convergence of the results performed in simulations using the Lorentz-boosted frame technique. This technique speeds up simulations by a large factor (36) while preserving their accuracy. The modelling work in this thesis has allowed analysis and understanding of experimental results, as well as prediction of results for future experiments. This thesis has also shown ways to optimize the injector to deliver an electron bunch that conforms with the specifications of future accelerators.

Diplomová práce se zabývá metodou hybridních (hranových a uzlových) konečných prvků ve frekvenční i časové oblasti. Tato metoda je použita pro analýzu vlnovodu parallel-plate, v kterém jsou umístěny dvě dielektrické vrstvy. Jako ukončení vlnovodu je implementována dokonale přizpůsobená vrstva označována PML. Projekt řeší možný výběr PML vrstvy v časové oblasti. Metoda je programována v programu MATLAB a výsledky jsou porovnány s programem COMSOL Multiphysics.