L'objectif principal de cette thèse est l'étude des problèmes et des applications qu'ils se développent dans le domaine de la nanophotonique. Plus précisément, nous considérons les structures de métaux nobles où les modèles de dispersion locaux sont insuffisants et la non-localité doit être incluse dans le modèle. Ici, le système physique sous-jacent est typiquement modélisé comme des équations de Maxwell couplées à des lois de dispersion spatio-temporelles dans le régime des longueurs d'onde optiques. Bien que les solutions analytiques puissent être dérivées pour un petit nombre de problèmes, cela n'est généralement pas possible pour les dispositifs du monde réel, qui présentent souvent des géométries complexes et des compositions de matériaux. Suite à une analyse rigoureuse des propriétés physiques et mathématiques du modèle continu original, nous proposons une méthode de type à éléments finis d'ordre élevé pour discrétiser le modèle continu dans l'espace et le temps. Les méthodes discontinues Galerkin (DG) sont bien établies pour la discrétisation spatiale des équations de Maxwell. Cette thèse prolonge les travaux antérieurs sur les systèmes couplés des équations de Maxwell et les lois de dispersion spatiale. Nous utilisons des méthodes explicites de Runge-Kutta (RK) d'ordre élevé pour la discrétisation temporelle. L'intégration temporelle RK garantit un ordre de convergence espace-temps élevé du schéma entièrement discret, qui repose sur un schéma de preuve de convergence. Parallélisme MPI (Message Passing Interface), éléments curvilignes et PML (Perfectly Matched Layers) autour des aspects d'implémentation et d'évaluation des performances dans le cadre du logiciel développé à Inria Sophia Antipolis-Méditerannée (DIOGENES). La méthode développée est appliquée à de nombreuses simulations nanophotoniques réelles de dispositifs où des observables tels que la réflexion, la section transversale (CS) et la spectroscopie de perte d'énergie électronique (EELS) sont étudiés. Entre autres, nous élaborons une feuille de route pour un étalonnage expérimental robuste du modèle de dispersion non local linéarisé basé sur la solution de problèmes inverses et la quantification d'incertitude (UQ) des paramètres géométriques stochastiques. Nous avons également amélioré les accords de simulations numériques non locales et les résultats expérimentaux pour la résonance des plasmons d'espacement des nano-cubes d'argent. Cela démontre la pertinence de simulations non locales précises. / The main objective of this thesis is the study of problems and applications as they arise in the field of nanophotonics. More speci cally, we consider noble metal structures where local dispersion models are insu cient and nonlocality has to be included in the model. Here, the underlying physical system is typically modeled as Maxwell’s equations coupled to spatio- temporal dispersion laws in the regime of optical wavelengths. While analytical solutions can be derived for a small number of problems, this is typically not possible for real-world devices, which often feature complicated geometries and material compositions. Following a rigorous analysis of the physical and mathematical properties of the original continuous model, we propose a high order finite element type method for discretizing the continuous model in space and time. Discontinuous Galerkin (DG) methods are well established for the spatial discretization of Maxwell’s equations. This thesis extends previous work on the coupled systems of Maxwell’s equations and spatial dispersion laws. We use explicit high-order Runge-Kutta (RK) methods for the subsequent time discretiz- ation. RK time integration guarantees a high space-time convergence order of the fully-discrete scheme, which is underpinned by a sketch of a convergence proof. Message Passing Interface (MPI) parallelization, curvilinear elements and Perfectly Matched Layers (PMLs) round of implementation aspects and performance assessments in the scope of the Software developed at Inria Sophia Antipolis-Méditerannée (DIOGENeS). The developed method is applied to numerous real-world nanophotonics simulations of devices where observables like re ectance, Cross Section (CS) and Electron Energy Loss Spectroscopy (EELS) are studied. Inter alia, we elaborate a roadmap for a robust experimental calibration of the linearized nonlocal disper- sion model based on the solution of inverse problems and Uncertainty Quanti cation (UQ) of stochastic geometric parameters. We also find improved agreements of nonlocal numerical simulations and exper- imental results for the gap-plasmon resonance of silver nano-cubes. This demonstrates the relevance of accurate nonlocal simulations.

Moment methods derived from the kinetic theory of gases can be used for the prediction of continuum and non-equilibrium flows and offer numerical advantages over other methods, such as the Navier-Stokes model. Models developed in this fashion are described by first-order hyperbolic partial differential equations (PDEs) with stiff local relaxation source terms. The application of discontinuous-Galerkin (DG) methods for the solution of such models has many benefits. Of particular interest is the third-order accurate, coupled space-time discontinuous-Galerkin Hancock (DGH) method. This scheme is accurate, as well as highly efficient on large-scale distributed-memory computers. The current study outlines a general implementation of the DGH method used for the parallel solution of moment methods in one, two, and three dimensions on modern distributed clusters. An algorithm for adaptive mesh refinement (AMR) was developed alongside the implementation of the scheme, and is used to achieve even higher accuracy and efficiency. Many different first-order hyperbolic and hyperbolic-relaxation PDEs are solved to demonstrate the robustness of the scheme. First, a linear convection-relaxation equation is solved to verify the order of accuracy of the scheme in three dimensions. Next, some classical compressible Euler problems are solved in one, two, and three dimensions to demonstrate the scheme's ability to capture discontinuities and strong shocks, as well as the efficacy of the implemented AMR. A special case, Ringleb's flow, is also solved in two-dimensions to verify the order of accuracy of the scheme for non-linear PDEs on curved meshes. Following this, the shallow water equations are solved in two dimensions. Afterwards, the ten-moment (Gaussian) closure is applied to two-dimensional Stokes flow past a cylinder, showing the abilities of both the closure and scheme to accurately compute classical viscous solutions. Finally, the one-dimensional fourteen-moment closure is solved.

We deal with the numerical solution of the Navier-Stokes equations describing a motion of viscous compressible flows. The governing equations are discretized with the aid of discontinuous Galerkin finite element method which is based on a discontinuous piecewise polynomial approximation. The discretizations leads to a large nonlinear algebraic system. In order to solve this system efficiently, we develop the so-called p-multigrid solution strategy which employ as a projec- tion and a restriction operators the L2 -projection in the spaces of polynomial functions on each element separately. The p-multigrid technique is studied, deve- loped and implemented in the code ADGFEM. The computational performance of the method is presented.

The development of computational fluid dynamics has given us a very powerful tool for investigation of fluid dynamics. However, in order to maintain the progress, it is necessary to improve the numerical algorithms. Nowadays, the high-order methods based on the discontinuous projection seem to have the largest potential for the future. In the work, we used open-source framework Nektar++, which provides the high-order discretization method. We tested the abilities of the framework for computing the compressible sonic and transonic flow. We successfully obtained simulations of the viscous and inviscid flow. We computed the lift and the drag coefficients and showed that for a higher polynomial order we can obtain the same accuracy with less degrees of freedom and lower computational time. Also, we tested the shock capturing method for the computation of the inviscid transonic flow and confirmed the potential of the high order methods. 1

A posteriori error estimation is an inseparable component of any reliable numerical method for solving partial differential equations. The aim of the goal-oriented a posteriori error estimates is to control the computational error directly with respect to some quantity of interest, which makes the method very convenient for many engineering applications. The resulting error estimates may be employed for mesh adaptation which enables to find a numerical approximation of the quantity of interest under some given tolerance in a very efficient manner. In this thesis, the goal-oriented error estimates are derived for discontinuous Galerkin discretizations of the linear scalar model problems, as well as of the Euler equations describing inviscid compressible flows. It focuses on several aspects of the goal-oriented error estimation method, in particular, higher order reconstructions, adjoint consistency of the discretizations, control of the algebraic errors arising from iterative solutions of both algebraic systems, and linking the estimates with the hp-anisotropic mesh adaptation. The computational performance is demonstrated by numerical experiments.

This thesis focuses on the study of magnetic properties of three 5f electron itinerant ferromagnets UCo0.990Ru0.010Al, UCoGa and URhGa and investigation of their phase diagrams. The single crystals of high-quality were prepared by Czochralski method for all three compounds. The physical properties at ambient pressure were studied by macroscopic methods (magnetization, electrical transport and heat capacity measurements) and also by magnetic force microscopy (MFM). The measurements were done under various external conditions (high pressure, low temperatures, high magnetic field). Through all these measurements and external conditions we investigated the interesting physical properties and the ferromagnetic phase diagrams. Effect of different conditions during the preparation and the thermal treatment on UCoGa was studied on two different single crystals. We show that annealing leads to improved quality of samples and the gallium evaporation from the melt during the growth leads to lower quality in parts of the ingot closer to melt. MFM images of UCoGa below the ordering temperature show domain branching and narrow magnetic domains wall made only of neighboring atoms with opposing moments. We have grown first ever single crystal of URhGa with ferromagnetic ordering temperature TC = 41 K. Anomalous maximum in...

A two-dimensional discontinuous Galerkin finite element method algorithm in the time domain was developed for calculation of the radar cross-section of an arbitrary object. The algorithm was formed using local nodal basis functions in each element and coupling them via numerical upwind flux. Both transverse electric and transverse magnetic polarization, as well as three different dispersive material models, were handled. The computational domain was effectively truncated with low reflections using the uniaxial perfectly matched layer method. Two different time stepping methods were used, low-storage explicit Runge-Kutta and Leap-Frog, to allow for flexibility in the time step and application of a stabilization method. The algorithm was verified with geometries, which have analytical expressions, and an existing validated code. The algorithm was also compared to an existing algorithm, which utilized the continuous finite element method with implicit time stepping, and showed outstanding performance regarding computation time and memory allocation. Since the developed algorithm had explicit time stepping could no general conclusions favoring any of the methods beyond these specific algorithms be made. The results still encouraged continued development of the DGFEM algorithm, where the expansion into three dimensions and optimizations could be explored further.

La fabrique du discontinu apparaît dans les romans des Goncourt sous différents aspects. Elle résulte de la formation des deux frères qui portent un intérêt particulier aux objets rares et aux détails. Se voulant modernes, les écrivains ne cessent de critiquer le roman idéaliste qu’ils considèrent comme une forme usée et montrent une préférence pour le modèle fantaisiste. Dans leur tentative de « tuer le romanesque », les auteurs de En 18.. font du roman un espace de liberté où ils n’hésitent pas à briser la linéarité du récit, à morceler la matière narrative en des petits chapitres, bref, à donner au lecteur un texte laconique qui sollicite sa collaboration. Constitué de plusieurs fragments du Journal, le roman des Goncourt devient le réservoir de textes de première main. La genèse de l’œuvre participe ainsi à la création de la discontinuité et engendre une grande diversité discursive et générique qui deviendra source de la modernité des romans goncourtiens. / The fashioning of the discontinuous takes various forms in the novels of Goncourt. It results from the construction of two brothers who have a particular interest in rare objects and details. In a bid to be modern, writers constantly criticize the idealist novel as a used form and show a preference for the whimsical model. In their attempt to "kill the romance", the authors of En 18 ..make the novel a space of freedom where they do not hesitate to break the linearity of the story, to break up the narrative material into small chapters, and to give the reader a terse text that solicits his collaboration. Consisting of several fragments of the Journal, the novel Goncourt becomes the reservoir of firsthand texts. The genesis of the work, thus, contributes to the creation of discontinuity and generates a great discursive and generic diversity that will become the source of the modernity of the Goncourt novels.

Indiana University-Purdue University Indianapolis (IUPUI) / The interplay between biomechanics and blood perfusion in the optic nerve head (ONH) has a critical role in ocular pathologies, especially glaucomatous optic neuropathy. Elucidating the complex interactions of ONH perfusion and tissue structure in health and disease using current imaging methodologies is difficult, and mathematical modeling provides an approach to address these limitations. The biophysical phenomena governing the ONH physiology occur at different scales in time and space and porous media theory provides an ideal framework to model them. We critically review fundamentals of porous media theory, paying particular attention to the assumptions leading to a continuum biphasic model for the phenomenological description of fluid flow through biological tissues exhibiting viscoelastic behavior. The resulting system of equations is solved via a numerical method based on a novel hybridizable discontinuous Galerkin finite element discretization that allows accurate approximations of stresses and discharge velocities, in addition to solid displacement and fluid pressure. The model is used to theoretically investigate the influence of tissue viscoelasticity on the blood perfusion of the lamina cribrosa in the ONH. Our results suggest that changes in viscoelastic properties of the lamina may compromise tissue perfusion in response to sudden variations of intraocular pressure, possibly leading to optic disc hemorrhages.

No description available.