Perfectly matched layer (PML) is a commonly used method of absorbing waves at a computational boundary for partial differential equation (PDE) problems. In this thesis, methods for improving the usability of implementations in Comsol Multiphysics is addressed. The study looks at complex coordinate stretching PMLs in the context of Helmholtz equation using the finite element method (FEM). For a PML to work it has to be set up properly with parameters that takes into account the properties of the problem. It is not always straight forward. Some theory behind PMLs is presented and experimentation on PML properties performed. Methods for PML optimization and adaption is presented. Currently, the way PMLs is applied in COMSOL Multiphysics requires the user to perform many tasks; setting up a geometry, meshing and choosing a suitable complex coordinate stretching. Using a so-called extra-dimension implementation it is possible to attach PMLs as boundary conditions in COMSOL Multiphysics. This simplifies for the user since the geometry and mesh is handled by the software. / Perfectly matched layer (PML) är en metod som ofta används för vågabsorbering vid randen för problem med partiella differentialekvationer (PDE). I det här examensarbetet presenteras metoder som förenklar användingen av PMLer i COMSOL Multiphysics. Studien kollar på PMLer baserade på komplex-koordinatsträckning med fokus på Helmholtz ekvation och finita elementmetoden (FEM). För att en PML ska fungera måste den sättas upp på rätt sätt med parametrar anpassade efter det givna problemet. Att göra detta är inte alltid enkelt. Teori presenteras och experiment på PMLer görs. Flera metoder för optimisering och adaption av PMLer presenteras. I nuläget kräver appliceringen av PMLer i COMSOL Multiphysics att användaren sätter upp en geometri, ett beräkningsnät och väljer den komplexa koordinatsträckningen. Genom att använda COMSOLs implementation av extra dimensioner är det möjligt att applicera PMLer som randvilkor. I en sådan implementation kan geometri och beräkningsnät skötas av mjukvaran vilket underlättar för användaren.

This thesis concerns dynamic Soil-Structure Interaction (SSI) analysis of portal framerailway bridges. Dynamic problems are common for bridges used for high speedrailway traffic. The passing trains induce harmonic loads on the bridges causingvibration amplitudes that may cause damage to the bridge structures and userdiscomfort.Previous studies have shown that the effects of SSI are substantial for short spanportal frame bridges. The damping ratio of the system is greatly increased due to theenergy dissipation properties of the surrounding soil causing significant changes in thedynamic response of the structure. Therefore, it is of interest to investigate the effectsof SSI for portal frame bridges with longer spans.Two case study bridges with span lengths of approximately 16m have been investigatedin detail in this study. Dynamic analyses of the bridges and train passage simulationshave been performed. The results show that SSI significantly increases the dampingratio which leads to lower vibration amplitudes. It is also possible to draw theconclusion that more accurate results are achieved when modeling fixed foundationsrather than using static spring foundations to replicate the stiffness of the subsoil.Moreover, a simplified modeling approach accounting for the effects of SSI is proposed.The proposed method provides satisfactory results, but more future work may increasethe quality of the results further. To validate the conclusions from this study, a proposalfor experimental validation is presented. Performing full-scale dynamic tests on thestudied bridges would enable further comparison and validation of the results.

This thesis explores the links between different ways of modelling the physical world. Finite difference numerical simulations may be used to encode the behaviour of physical systems, allowing us to gain insight into their workings and even to predict their behaviour. Similarly, one can investigate the properties of gravitational black holes through the use of analogue black holes, physical systems which share at least some part of the physics of the astronomical objects. Concentrating on black hole analogues using Bose-Einstein condensates, I show how simulations of these systems may be greatly assisted through the use of a proper absorbing boundary condition, the Perfectly Matched Layer. Such a boundary condition allows the effcient truncation of the computational domain, both saving computational time and increasing accuracy. I then apply this technique to the simulation of the supersonic flow of a Bose-Einstein condensate through a Laval nozzle, a black hole analogue, showing that such a flow should be stable and observable in the laboratory. Moving to a related system, I investigate the optical analogue of the Iordanskii force - the friction resulting from interaction between excitations in a superfluid's normal component and a superfluid vortex - through the simulation of such a vortex in a Bose-Einstein condensate illuminated by slow light, which is light whose group velocity is on the order of metres per second. The interaction of the slow light with the vortex should produce a momentum transfer due to the optical Aharonov-Bohm effect, exerting a force on the vortex. The coupled system of equations describing the condensate-slow light system is simulated, giving some surprising results.

De nombreux éléments de structures de génie civil sont élancés et partiellement enfouis dans un milieu solide. Les ondes guidées sont souvent utilisées pour le contrôle non destructif (CND) de ces éléments. Ces derniers sont alors considérés comme des guides d’ondes ouverts, dans lesquels la plupart des ondes sont atténuées par des fuites dans le milieu environnant. D’autre part le problème est non borné, ce qui le rend difficile à appréhender sur le plan numérique. La combinaison d’une approche par éléments finis semi-analytique (SAFE) et de la méthode des couches parfaitement adaptées (PML) a été utilisée dans une thèse antérieure pour calculer numériquement trois types de modes (modes piégés, modes à fuite et modes de PML). Seuls les modes piégés et à fuite sont utilisés pour la représentation des courbes de dispersion. Les modes de PML sont non intrinsèques à la physique. L’objectif premier de cette thèse est d’obtenir, par superposition modale sur les modes calculés, les champs émis et diffracté dans les guides d’ondes ouverts. Nous montrons dans un premier temps que les trois types de modes appartiennent à la base modale. Une relation d’orthogonalité est obtenue dans la section du guide(incluant la PML) pour garantir l’unicité des solutions. La réponse forcée du guide peut alors être calculée rapidement par une somme sur les modes en tout point du guide. Des superpositions modales sont également utilisées pour construire des frontières transparentes au bord d’un petit domaine élément fini incluant un défaut, permettant ainsi de calculer le champ diffracté. Au cours de ces travaux, nous étudions les conditions d’approximation des solutions par des superpositions modales, limitées seulement aux modes à fuite, ce qui permet de réduire le coût des calculs. De plus, la généralité des méthodes proposées est démontrée par des calculs hautes fréquences (intéressantes pour le CND) et sur des guides tridimensionnels. Le deuxième objectif de cette thèse est de proposer une méthode d’imagerie pour la localisation de défauts. La méthode de l’imagerie topologique est appliquée aux guides d’ondes. Le cadre théorique général, de type optimisation sous contrainte, est rappelé. Le formalisme modal permet un calcul rapide de l’image. Nous l’appliquons pour simuler un guide d’onde endommagé, et nous montrons l’influence du type de champ émis (monomodal, dispersif,multimodal) ainsi que des configurations de mesure sur la qualité de l’image obtenue. / Various elements of civil engineering structures are elongated and partially embedded in a solid medium. Guided waves can be used for the nondestructive evaluation (NDE) of such elements. The latteris therefore considered as an open waveguide, in which most of waves are attenuated by leakage losses into the surrounding medium. Furthermore, the problem is difficult to solve numerically because of its unboundedness. In aprevious thesis, it has been shown that the semi-analytical finite-element method (SAFE) and perfectly matched layers(PML) can be coupled for the numerical computation of modes. It yields three types of modes: trapped modes,leaky modes and PML modes. Only trapped and leaky modes are useful for the post-processing of dispersion curves. PML modes are non-intrinsic to the physics. The major aim of this thesis is to obtain the propagated and diffracted fields, based on modal superpositions on the numerical modes. First, we show that the three types of modes belong to the modal basis. To guarantee the uniqueness of the solutions an orthogonality relationship is derived on the section including the PML. The forced response can then be obtained very efficiently with a modal expansion at any point of the waveguide. Modal expansions are also used to build transparent boundaries at the cross-sections of a small finite-element domain enclosing a defect, thereby yielding the diffracted field. Throughout this work, we study whether solutions can be obtained with modal expansions on leaky modes only, which enables to reduce the computational cost. Besides, solutions are obtained at high frequencies (which are of interest for NDE) and in tridimensional waveguides, which demonstrates the generality of the methods. The second objective of this thesis is to propose an imaging method to locate defects. The topological imaging method is applied to a waveguide configuration. The general theoretical framework is recalled, based on constrained optimization theory. The image can be quickly computed thanks to the modal formalism. The case of a damaged waveguide is then simulated to assess the influence on image quality of the emitted field characteristics (monomodal, dispersive or multimodal)and of the measurement configuration.

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.

Existing unified numerical electromagnetic methods are often unable to analyze electrically large structures due to the amount of memory and processing power required, necessitating approximate analyses with limited applicability. In this research a hybrid modeling methodology is adopted to solve these complex problems more efficiently than unified numerical methods and more accurately than analytical methods. Electromagnetic modeling problems are divided into two or more levels of scale. Each level analyzes a specific level of detail and only promotes the required information to the next level. The method is demonstrated by successful application to three important problems: (1) remote sensing of snow, (2) modeling an optical Bragg resonator, and (3) modeling the MIMO wireless channel. First, complex snow media is analyzed with a hybrid FDTD/radiative transfer model. FDTD is used to compute phase matrices and extinction coefficients required for radiative transfer. Comparison with exact analytical methods proves the validity of the FDTD method for modest domain sizes ([5λ^3]) and number of Monte Carlo realizations (32). The method is used to illustrate a penetrating sphere model, which is not possible with existing analysis techniques. Backscatter from the resulting model is about 3 times higher than that of existing dense-medium theories, underlying the importance of exact characterization of the media. Second, a hybrid FD/FDTD/S-parameter analysis is developed to model a large (10^4 section) optical Bragg resonator: a simple FD method computes propagation constants and field profiles, FDTD analysis provides reflection and transmission coefficients for the single section, and S-parameter analysis combines the sections to obtain the complete device response. A detailed study on error suggests that the method provides better than 2% accuracy in reflection and transmission response. Third, a hybrid electromagnetic/SVA model is developed to study the indoor MIMO wireless channel. A MIMO measurement platform is discussed for simultaneous probing of up to 16 transmit and receive antennas, which was required to assess the validity of later modeling. FDTD or MOM antenna analysis coupled with the SVA model gives capacity predictions which match measured data. The model is used to explore the impact of antenna spacing, directivity, and polarization on channel capacity. Closely spaced antennas lead to an approximate halving of receive power. Directivity effectively doubles receive power for aligned transmit and receive. Dual polarization increases system capacity anywhere from 10% to 70%, depending on the spacing of elements and the amount of multipath richness. This analysis of MIMO systems underlines the need for models that describe both multipath richness and average receive power.

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.

The work considers pulse wire-guided electromagnetic (EM) waves. The main contribution of the work is the original design of the isolation bushing for maximizing of the received wave (echo) thanks to the results of the numerical simulations, the acquirement of the new acknowledges of the reflections of the guided EM wave from the various boundaries, the construction of PML layers for FDTD simulations in rotational coordinates, the advances made in temporary excitation sources for FDTD and the formulation of the program code for FDTD in rotational coordinates in Matlab environment. The rightness of the numerical simulations was verified in practical experiments. The practical exploitation of the results is supposed in instrumentation and control technology - the level measurement in reservoirs.