Se trata el problema de consolidación bidimensional de arcillas blandas saturadas a partir de un estado inicial producido por un proceso de carga sin drenaje. Se elabora un modelo en tensiones efectivas que define el comportamiento del suelo como un material elastoplástico isótropo rigidizable del tipo no-asociado. Se desarrolla un método de análisis que tiene en cuenta la variación de las tensiones totales durante la consolidación mediante un procedimiento iterativo admitiendo la posibilidad de considerar el terreno heterogéneo con permeabilidad anisótropa y carga variable con el tiempo. La resolución se lleva a cabo por el método de elementos finitos. Se analiza un caso típico teórico y un caso real comparando en este ultimo los resultados obtenidos y las medidas efectuadas. / A model is presented for the analysis of consolidation problems of soft clays. The soil is treated as an elastoplastic material, strain hardening and with a flow rule of non-associated type. The numerical analysis is performed by a finite element method, in which the consolidation and effective stress-strain analyses are performed separately and then coupled by means of an iterative method. The case of a strip footing on the surface of a clay layer is analyzed. The influence of the soil stress-strain properties is evaluated, as well as the permeability anisotropy and the load variation with time.

Se discute la guía dieléctrica en banda invertida como modificación capaz de aumentar el factor de calidad de la guía dieléctrica rectangular. En su configuración abierta se emplea para su estudio el método de la constante dieléctrica efectiva; se optimiza la geometría para conseguir el mayor ancho de banda posible y se discute la posibilidad de naturaleza espuerea para una parte de los modos encontrados. Se comprueba que el sistema de excitación clásico para guías dieléctricas no resulta valido para la guía en banda invertida y se optimiza un sistema de tipo cornete. Mediante un sistema de sonda móvil se mide la constante de propagación en la guía obteniéndose un buen acuerdo con las predicciones teóricas. Se estudia la guía dieléctrica cerrada en una caja mediante el método de Schelkunoff comprobándose la existencia de modos EH. / The inverted band dielectric waveguide is proposed as an alternative to the classical open dielectric waveguide, providing a higher quality factor. The dielectric effective constant method is used to study the open waveguide. In order to get the highest bandwith, the geometry is optimised, finding not real modes in the waveguide. It has been necessary to use a new excitation method of waveguide using a horn as transition. The measurement of the propagation constant has been made by means of an electric probe. The agreement with the theoretical predictions is very good. Finally the closed guide is studied by the Schelkunoff's method: modes EH were observed.

In the thesis, the Wilcoxon approach to linear regression problems is combined with the fractal image compression to form a novel Wilcoxon fractal image compression. When the original image is corrupted by noise, we argue that the fractal image compression scheme should be insensitive to those outliers present in the corrupted image. This leads to the new concept of robust fractal image compression. The proposed Wilcoxon fractal image compression is the first attempt toward the design of robust fractal image compression. Four different numerical methods, i.e., steepest decent, line minimization based on quadratic interpolation, line minimization based on cubic interpolation, and least absolute deviation, will be proposed to solve the associated linear Wilcoxon regression problem. From the simulation results, it will be seen that, compared with the traditional fractal image compression, Wilcoxon fractal image compression has very good robustness against outliers caused by salt-and-pepper noise. However, it does not show great improvement of the robustness against outliers caused by Gaussian noise.

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In a first part, we are interested in the behavior of a system of Stochastic PDEs with two time-scales- more precisely, we focus on the approximation of the slow component thanks to an efficient numerical scheme. We first prove an averaging principle, which states that the slow component converges to the solution of the so-called averaged equation. We then show that a numerical scheme of Euler type provides a good approximation of an unknown coefficient appearing in the averaged equation. Finally, we build and we analyze a discretization scheme based on the previous results, according to the HMM methodology (Heterogeneous Multiscale Method). We precise the orders of convergence with respect to the time-scale parameter and to the parameters of the numerical discretization- we study the convergence in a strong sense - approximation of the trajectories - and in a weak sense - approximation of the laws. In a second part, we study a method for approximating solutions of parabolic PDEs, which combines a semi-lagrangian approach and a Monte-Carlo discretization. We first show in a simplified situation that the variance depends on the discretization steps. We then provide numerical simulations of solutions, in order to show some possible applications of such a method.

Nowadays there is an ever increasing demand to obtain more accurate numericalsimulation results while at the same time using fewer computations. One area withsuch a demand is oil reservoir simulations, which builds upon Poisson's equation withvariable coefficients (PEWVC). This thesis focuses on applying and testing a high ordernumerical scheme to solve the PEWVC, namely Summation By Parts - SimultaneousApproximation Term (SBP-SAT). The thesis opens with proving that the method isconvergent at arbitrary high orders given sufficiently smooth coefficients. Theconvergence is furthermore verified in practice by test cases on the Poisson'sequation with smoothly variable permeability coefficients. To balance observed lowerboundary flux convergence, the SBP-SAT method was modified with additionalpenalty terms that were subsequently shown to work as expected. Finally theSBP-SAT method was tested on a semi-realistic model of an oil reservoir withdiscontinuous permeability. The correctness of the resulting pressure distributionvaried and it was shown that flux leakage was the probable cause. Hence theproposed SBP-SAT method performs, as expected, very well in continuous settingsbut typically allows undesirable leakage in discontinuous settings. There are possiblefixes, but these are outside the scope of this thesis.

In this thesis we investigate numerical methods for the homogenization of materials the structures of which, at fine scales, are characterized by random heterogenities. Under appropriate hypotheses, the effective properties of such materials are given by closed formulas. However, in practice the computation of these properties is a difficult task because it involves solving partial differential equations with stochastic coefficients that are additionally posed on the whole space. In this work, we address this difficulty in two different ways. The standard discretization techniques lead to random approximate effective properties. In Part I, we aim at reducing their variance, using a well-known variance reduction technique that has already been used successfully in other domains. The works of Part II focus on the case when the material can be seen as a small random perturbation of a periodic material. We then show both numerically and theoretically that, in this case, computing the effective properties is much less costly than in the general case

Tagungsband des Ohde-Kolloquiums 2014. Die Fachtagung fand am 26.03.2014 an der TU Dresden statt.

We elaborate upon the Herty-Illner macroscopic traffic models which include special non-local forces. The first chapter presents these in relation to the traffic models of Aw-Rascle and Zhang, arguing that non-local forces are necessary for a realistic description of traffic. The second chapter considers travelling wave solutions for the Herty-Illner macroscopic models. The travelling wave ansatz for the braking scenario reveals a curiously implicit nonlinear functional differential equation, the jam equation, whose unknown is, at least to conventional tools, inextricably self-argumentative! Observing that analytic solution methods fail for the jam equation yet succeed for equations with similar coefficients raises a challenging problem of pure and applied mathematical interest. An unjam equation analogous to the jam equation explored by Illner and McGregor is derived. The third chapter outlines refinements for the Herty-Illner models. Numerics allow exploration of the refined model dynamics in a variety of realistic traffic situations, leading to a discussion of the broadened applicability conferred by the refinements: ultimately the prediction of stop-and-go waves. The conclusion asserts that all of the above contribute knowledge pertinent to traffic control for reduced congestion and ameliorated vehicular flow. / Graduate

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