Étant donné que le stockage de gaz naturel ou d’air comprimé dans des niveaux souterrains constitués de sel joue un rôle essentiel pour assurer l'approvisionnement en énergie sur le long terme, le gouvernement chinois a construit de nombreux lieu de stockage dans ces niveaux géologiques ces dernières années. En raison des variations saisonnières de la pression gaz / air, les entrepôts subissent des chargements cycliques qui provoquent la fatigue des roches et conduisent à des risques de rupture qu’il faut maîtriser pour des raisons liées à la sécurité et à l'environnement. La compréhension des processus de fatigue discontinue du sel sous chargement cyclique est donc très importante et fait l'objet de cette étude, qui se concentre sur des recherches expérimentales et le développement de modèles constitutifs décrivant la déformation sous fatigue. Cette thèse s’articule suivant la méthodologie suivante : ① des essais de chargement cyclique classique pour étudier les propriétés basiques de la fatigue dans le sel. ② des tests de charge cyclique discontinu pour explorer les processus de fatigue discontinue. ③ l’instrumentation pour détecter les émissions acoustiques afin de suivre l'évolution des dommages causés par la fatigue dans le sel. ④ Le développement à la base des résultats expérimentaux obtenus de modèle constitutif pour la fatigue discontinue. / Since the salt cavern storage of natural gas and compressed air plays a critical role in ensuring the energy supply and adjusting the seasonal imbalance of power, China government has been constructing numerous new storages in recent years. Because of the seasonal of the seasonal variations of the gas/air pressure, the storages undergo cyclic loading, which causes rock fatigue and induces the associated safety and environmental hazards. The investigation of the discontinuous fatigue of salt under cyclic loading is therefore very important and is the subject of this study, which focuses on the experimental investigations and the development of the constitutive models describing the fatigue deformation. This thesis includes the following principal parts: ① Conventional cyclic loading testing to investigate the basic properties of fatigue in salt. ② Discontinuous cyclic loading tests testing to investigate the discontinuous fatigue. ③ Acoustic emission detecting experimentation to track the evolution of the fatigue damage in the salt. ④ Development of the fatigue life model and constitutive model for the discontinuous fatigue, based on the obtained experimental results.

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A triangular B-spline (DMS-spline)-based finite element method (TBS-FEM) is proposed along with possible enrichment through discontinuous Galerkin, continuous-discontinuous Galerkin finite element (CDGFE) and stabilization techniques. The developed schemes are also numerically explored, to a limited extent, for weak discretizations of a few second order partial differential equations (PDEs) of interest in solid mechanics. The presently employed functional approximation has both affine invariance and convex hull properties. In contrast to the Lagrangian basis functions used with the conventional finite element method, basis functions derived through n-th order triangular B-splines possess (n ≥ 1) global continuity. This is usually not possible with standard finite element formulations. Thus, though constructed within a mesh-based framework, the basis functions are globally smooth (even across the element boundaries). Since these globally smooth basis functions are used in modeling response, one can expect a reduction in the number of elements in the discretization which in turn reduces number of degrees of freedom and consequently the computational cost. In the present work that aims at laying out the basic foundation of the method, we consider only linear triangular B-splines. The resulting formulation thus provides only a continuous approximation functions for the targeted variables. This leads to a straightforward implementation without a digression into the issue of knot selection, whose resolution is required for implementing the method with higher order triangular B-splines. Since we consider only n = 1, the formulation also makes use of the discontinuous Galerkin method that weakly enforces the continuity of first derivatives through stabilizing terms on the interior boundaries. Stabilization enhances the numerical stability without sacrificing accuracy by suitably changing the weak formulation. Weighted residual terms are added to the variational equation, which involve a mesh-dependent stabilization parameter. The advantage of the resulting scheme over a more traditional mixed approach and least square finite element is that the introduction of additional unknowns and related difficulties can be avoided. For assessing the numerical performance of the method, we consider Navier’s equations of elasticity, especially the case of nearly-incompressible elasticity (i.e. as the limit of volumetric locking approaches). Limited comparisons with results via finite element techniques based on constant-strain triangles help bring out the advantages of the proposed scheme to an extent.

In this dissertation, we study integrodifference equations in patchy landscapes. Specifically, we provide a framework for linking individual dispersal behavior with population-level dynamics in patchy landscapes by integrating recent advances in modeling dispersal into an integrodifference equation. First, we formulate a random-walk model in a patchy landscape with patch-dependent diffusion, settling, and mortality rates. We incorporate mechanisms for individual behavior at an interface which, in general, results in the probability-density function of the random walker being discontinuous at an interface. We show that the dispersal kernel can be characterized as the Green's function of a second-order differential operator and illustrate the kind of (discontinuous) dispersal kernels that arise from our approach. We examine the dependence of obtained kernels on model parameters. Secondly, we analyze integrodifference equations in patchy landscapes equipped with discontinuous kernels. We obtain explicit formulae for the critical-domain-size problem, as well as, explicit formulae for the analogous critical size of good patches on an infinite, periodic, patchy landscape. We examine the dependence of obtained formulae on individual behavior at an interface. Through numerical simulations, we observe that, if the population can persist on an infinite, periodic, patchy landscape, its spatial profile can evolve into a discontinuous traveling periodic wave. We derive a dispersion relation for the speed of the wave and illustrate how interface behavior affects invasion speeds. Lastly, we develop a strategic model for the spread of the emerald ash borer and its interaction with host trees. A thorough literature search provides point estimates and interval ranges for model parameters. Numerical simulations show that the spatial profile of an emerald ash borer invasion evolves into a pulse-like solution that moves with constant speed. We employ Latin hypercube sampling to obtain a plausible collection of parameter values and use a sensitivity analysis technique, partial rank correlation coefficients, to identify model parameters that have the greatest influence on obtained speeds. We illustrate the applicability of our framework by exploring the effectiveness of barrier zones on slowing the spread of the emerald ash borer invasion.

Voluntary coughs are used as a diagnostic tool to detect lung diseases. Understanding the mechanics of a cough is therefore crucial to accurately interpreting the test results. A cough is characterised by a dynamic compression of the airways, resulting in large flow velocities and producing transient peak expiratory flows. Existing models for pulmonary flow have one or more of the following limitations: 1) they assume quasi-steady flows, 2) they assume low speed flows, 3) they assume a symmetrical branching airway system. The main objective of this thesis is to develop a model for a cough in the branching pulmonary airway system. First, the time-dependent one-dimensional equations for flow in a compliant tube is used to simulate a cough in a single airway. Using anatomical and physiological data, the tube law coupling the fluid and airway mechanics is constructed to accurately mimic the airway behaviour in its inflated and collapsed states. Next, a novel model for air flow in an airway bifurcation is constructed. The model is the first to capture successfully subcritical and supercritical flows across the bifurcation and allows for free time evolution from one case to another. The model is investigated by simulating a cough in both symmetric and asymmetric airway bifurcations. Finally, a cough model for the complete branching airway system is developed. The model takes into account the key factors involved in a cough; namely, the compliance of the lungs and the airways, the coughing effort and the sudden opening of the glottis. The reliability of the model is assessed by comparing the model predictions with previous experimental results. The model captures the main characteristics of forced expiatory flows; namely, the flow limitation phenomenon (the flow out of the lungs becomes independent of the applied expiratory effort) and the negative effort dependence phenomenon (the flow out of the lungs decreases with increasing expiratory effort). The model also gives a good qualitative agreement with the measured values of airway resistance. The location of the collapsed airway segment during forced expiration is, however, inconsistent with previous experimental results. The effect of changing the model parameters on the model predictions is therefore discussed.

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element methods are used. Error and stability analysis is presented for some of the methods. Numerical examples suggest that all three methods exhibit very similar convergence properties, consistent with available theoretical results.:1. Introduction 2. Model Problem and Background 3. New Coupling Methods 4. Stability and Error Analysis 5. Numerical Examples 6. Summary A. Appendix

The compressible Euler equations describe the motion of compressible inviscid fluids. They are used in many areas ranging from aerospace, automotive, and nuclear engineering to chemistry, ecology, climatology, and others. Mathematically, the compressible Euler equations represent a hyperbolic system consisting of several nonlinear partial differential equations (conservation laws). These equations are solved most frequently by means of Finite Volume Methods (FVM) and low-order Finite Element Methods (FEM). However, both these approaches are lacking higher order accuracy and moreover, it is well known that conforming FEM is not the optimal tool for the discretization of first-order equations. The most promissing approach to the approximate solution of the compressible Euler equations is the discontinuous Galerkin method that combines the stability of FVM, with excellent approximation properties of higher-order FEM. The objective of this Master Thesis was to develop, implement and test new adaptive algorithms for the nonstationary compressible Euler equations based on higher-order discontinuous Galerkin (hp-DG) methods. The basis for the new methods were the discontinuous Galerkin methods and space-time adaptive hp-FEM algorithms on dynamical meshes for nonstationary second-order problems. The new algorithms...

Die Nanooptik beschäftigt sich mit der Wechselwirkung von Licht mit Materie, deren charakteristische Dimension im Nanometer Bereich liegt. Insbesondere wenn die Materie aus Metall besteht, zeigen sich interessante, wellenlängenabhängige Unterschiede in der Stärke der Wechselwirkung. Die Ursache dafür sind die kollektiven Moden der quasifreien Ladungsträger, die Plasmonen. Obgleich sich experimentelle Methoden in den letzten Jahren stetig verbessert haben, ist es nach wie vor nur mit erheblichem Aufwand möglich, sich Einblicke in die mikroskopischen Zusammenhänge zu verschaffen. Eine Ergänzung zu den Experimenten bieten theoretische Modelle. Auf Grund der sich mit der Zeit stetig verbesserten Leistung der Rechentechnik, kommen dabei zunehmend numerische Verfahren zum Einsatz. Eines dieser Verfahren ist das Unstetige Galerkin Verfahren, welches in dieser Arbeit auf folgende Fragestellungen der plasmonischen Nanooptik angewandt wurde: • Bei dem unstetigen Galerkin Verfahren werden die zu simulierenden Körper üblicherweise mittels Dreiecke und Tetraeder approximiert. Da die Geometrie der metallischen Systeme einen entscheidenden Einfluss auf die Wechselwirkung hat, wurde untersucht, inwieweit sich durch Einsatz von Elementen mit gekrümmten Flächen die Genauigkeit oder die Geschwindigkeit der Simulation steigern lässt. Es konnte gezeigt werden, dass runde Elemente die Genauigkeit bei gleicher Diskretisierung um bis zu zwei Größenordnungen steigern oder die Rechenzeit bei gleicher Genauigkeit auf ein Sechstel verkürzen können. • Bestrahlt man Metallnanopartikel mit intensiven Laserpulsen, so strahlen diese nicht nur bei der Frequenz des eingestrahlten Lichtes, sondern auch bei der doppelten Frequenz ab. Dieses Phänomen der Frequenzverdopplung (SHG, engl.: „Second-Harmonic-Generation“) ist unter anderem von der Form der Partikel und der Wellenlänge des Pulses abhängig. Da durchstimmbare gepulste Laser sehr teuer sind, wurde untersucht, ob sich mit Hilfe der linearen Partikelspektren Vorhersagen über die Stärke der Frequenzverdopplung machen lassen. Dabei wurde festgestellt, dass die Effizienz der Frequenzverdopplung zunimmt, wenn man die linearen Resonanzen der Partikel auf die SHG- oder Anregungswellenlänge abstimmt. Schafft man es, das plasmonische System so einzustellen, dass sowohl die Anregungswellenlänge, wie auch die SHG- Wellenlänge auf einer linearen Resonanz liegen, so kann die Effizienz der SHG weiter gesteigert werden. / Nanooptics is a discipline dealing with the interaction of light with matter where its characteristic dimensions are defined to be in the range of nanometers. In particular, if the matter consists of metal, i.e. conductive material, interesting wavelength dependent phenomena can be observed, which scale with the strength of the interaction. These phenomena are caused by the formation of collective modes between quasi-free charge carriers resulting in so called plasmons. Although improved experimental methods have evolved over the last few years, insight into the microscopic relationship between light and matter is only achievable with high effort. Supplemental information to experimental findings can be drawn from theoretical models. Due to the constantly improving computational power, numerical methods are progressively more employed. One of these methods is the discontinuous Galerkin method, which was applied to the following problems in plasmonic nanooptics: • Within the discontinuous Galerkin method the simulated objects are usually approximated by triangles or tetrahedrons. Since the geometry of conductive systems has a major impact on the interaction between light and matter, the usability of elements with curved surfaces for the discretisation of the space has been investigated with respect to accuracy and speed of the simulation. In this work, it could be shown that curved elements improve the simulations precision up to two orders of magnitude with the same amount of discretisation compared to linear elements. Related to speed, it has been found that the computational time is reduced by a factor of 6 with a comparable simulation accuracy. • By irradiating metallic nanoparticles with high power laser pulses these particles do not only emit light of the same frequency as the incident electromagnetic wave, but also with the doubled frequency (SHG, second harmonic generation). Among other things, this phenomenon of frequency doubling mainly depends on the geometry of the particle and the wavelength of the pulse. Since tunable pulsed laser sources are very expensive, it has been theoretically investigated if the strength of the frequency doubling can be deduced from the particles linear spectra. By this, it has been discovered that the efficiency of frequency doubling can be improved by adjusting the linear resonances of the particle to the SHG or excitation wavelength. The SHG efficiency can be increased even further, if the plasmonic system is tuned to a point where both the excitation and the SHG wavelength correspond to a linear resonance of the nanoparticle.

Cette thèse traite de la résolution du système de la Magnéto-Hydro-Dynamique (MHD) sur architectures massivement parallèles. Ce système est un système hyperbolique de lois de conservation. Pour des raisons de coût en termes de temps et d'espace, nous utilisons la méthode des volumes finis. Ces critères sont particulièrement importants dans le cas de la MHD, car les solutions obtenues peuvent présenter de nombreuses ondes de choc et être très turbulentes. L'approche d'un phénomène physique nécessite par conséquent de travailler sur un maillage fin entrainant une grande quantité de calcul. Afin de réduire les temps d'exécution des algorithmes proposés, nous proposons des méthodes d'optimisations pour l'exécution sur CPU telles que l'utilisation d'OpenMP pour une parallélisation automatique ou le parcours optimisé afin de bénéficier des effets de cache. Une implémentation sur architecture GPU à l'aide de la librairie OpenCL est également proposée. Dans le but de conserver une coalescence maximale des données en mémoire, nous proposons une méthode utilisant un splitting directionnel associé à une méthode de transposition optimisée pour les implémentations parallèle. Dans la dernière partie, nous présentons la librairie SCHNAPS. Ce solveur utilisant la méthode Galerkin Discontinu (GD) utilise des implémentations OpenCL et StarPU afin de profiter au maximum des avantages de la programmation hybride. / This thesis deals with the resolution of the Magneto-Hydro-Dynamic (MHD) system on massively parallel architectures. This problem is an hyperbolic system of conservation laws. For cost reasons in terms of time and space, we use the finite volume method. These criteria are particularly important in the case of MHD because the solutions obtained may have many shock waves and be very turbulent. The approach of a physical phenomenon requires working on a fine mesh which involves a large quantity of computations. In order to reduce the execution time of the proposed algorithms, we present several optimization methods for CPU execution such as the use of OpenMP for an automatic parallelization or an optimized way to browse a grid in order to benefit from cache effects. An implementation on GPU architecture using the OpenCL library is also available. To maintain a maximal coalescence of the data in memory, we propose a method using a directional splitting associated with an optimized transposition method for parallel implementations. In the last part, we present the SCHNAPS library. This solver using the Galerkin Disontinu (GD) method uses OpenCL and StarPU implementations in order to maximize the benefits of hybrid programming.

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第21374号 / 農博第2298号 / 新制||農||1066(附属図書館) / 学位論文||H30||N5147(農学部図書室) / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 村上 章, 教授 藤原 正幸, 教授 渦岡 良介 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM