<p>In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction.</p><p>In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view.</p><p><b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering</p>

Numerical simulation methods have become an important tool in the study of chemical reaction networks in living cells. Many systems can, with high accuracy, be modeled by deterministic ordinary differential equations, but other systems require a more detailed level of modeling. Stochastic models at either the mesoscopic level or the microscopic level can be used for cases when molecules are present in low copy numbers. In this thesis we develop efficient and flexible algorithms for simulating systems at the microscopic level. We propose an improvement to the Green's function reaction dynamics algorithm, an efficient microscale method. Furthermore, we describe how to simulate interactions with complex internal structures such as membranes and dynamic fibers. The mesoscopic level is related to the microscopic level through the reaction rates at the respective scale. We derive that relation in both two dimensions and three dimensions and show that the mesoscopic model breaks down if the discretization of space becomes too fine. For a simple model problem we can show exactly when this breakdown occurs. We show how to couple the microscopic scale with the mesoscopic scale in a hybrid method. Using the fact that some systems only display microscale behaviour in parts of the system, we can gain computational time by restricting the fine-grained microscopic simulations to only a part of the system. Finally, we have developed a mesoscopic method that couples simulations in three dimensions with simulations on general embedded lines. The accuracy of the method has been verified by comparing the results with purely microscopic simulations as well as with theoretical predictions. / eSSENCE

This work is focused on the development of a hybrid DSMC/CFD solver to examine hypersonic boundary layer flow over discrete surface roughness. The purpose of these investigations is to identify and quantify the non-equilibrium effects that influence the roughness-induced disturbance field and surface quantities of interest for engineering applications. To this end, a new hybrid framework is developed for high-fidelity hybrid solutions involving five-species air hypersonic boundary layer flow applications. A novel approach is developed for DSMC particle generation at a hybrid interface for gas mixtures with internal degrees of freedom. The appropriate velocity distribution function is formulated in the framework of Generalized Chapman-Enskog Theory, and includes contributions from species mass diffusion, shear stress and heat fluxes (both translational and internal) on the perturbation of the equilibrium distribution function. This formulation introduces new breakdown parameters for use in hybrid DSMC/CFD applications, and the new sampling algorithm allows for the generation of DSMC internal energies from the appropriate non-equilibrium distribution for the first time in the literature. The contribution of the internal heat fluxes to the overall perturbation is found to be of the same order as the stress tensor components, underscoring the importance of DSMC particle generation from the Generalized Chapman-Enskog distribution. A detailed comparison of the transport coefficients is made between the DSMC and CFD solvers, and a general best-fit approach is developed for the consistent treatment of diffusion, viscosity and thermal conductivity for a five-species air gas mixture. The DSMC VHS/VSS model parameters are calibrated through an iterative fitting approach using the Nelder-Mead Simplex Algorithm. The VSS model is found to provide the best fit (within 5% over the temperature range) to the transport models used in the CFD solver. The best-fit five-species air parameters are provided for general use by the DSMC community, either for hybrid applications or to provide improved consistency in general DSMC/CFD applications. This hybrid approach has been applied to examine hypersonic boundary layer flow over discrete surface roughness for a variety of roughness geometries and flow conditions. An (asymmetric) elongated hump geometry and (symmetric) diamond shaped roughness geometry are examined at high and low altitude conditions. Detailed comparisons among the hybrid solution and the CFD no-slip and slip wall solutions were made to examine the differences in surface heating, translational/vibrational non-equilibrium in the flow near the roughness, and the vortex structures in the wake through the Q-criterion. In all cases examined, the hybrid solution predicts a lower peak surface heating to the roughness compared to either CFD solution, and a higher peak surface heating in the wake due to vortex heating. The observed differences in vortex heating are a result of the predicted vortex structures which are highlighted using the Q-criterion. The disturbance field modeled by the hybrid solution organizes into a system of streamwise-oriented vortices which are slightly stronger and have a greater spanwise extent compared to the CFD solutions. As a general trend, it was observed that these differences in the predicted heating by the hybrid and CFD solutions increase with increasing Knudsen number. This trend is found for both peak heating values on the roughness and in the wake. / text

In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction. In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view. <b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering / NR 20140805

O problema de dimensionamento de lotes determina um plano de produção que apoia às tomadas de decisões, a médio prazo, em meios industriais. Este plano de produção indica as quantidades de cada item que devem ser produzidas em cada período do horizonte de planejamento, de acordo com um objetivo dado e satisfazendo a demanda dos clientes. Diversos métodos de solução foram propostas na literatura, considerando a dificuldade de solução de algumas classes de problemas e a necessidade de métodos que gerem soluções de alta qualidade em um tempo computacional adequado. Neste trabalho, abordamos heurísticas baseadas na formulação matemática (LP-and-fix, relax-and-fix e fix-and-optimize), uma metaheurística (algoritmo de abelhas) e dois métodos híbridos, utilizados na solução de dois problemas distintos de dimensionamento de lotes multiestá- gio com limitação de capacidade. Consideramos também, a utilização de três formulações da literatura, para verificar a influência de cada uma sobre as abordagens de solução verificadas. Os resultados computacionais demonstraram que os métodos baseados na formulação matemática do problema se mostraram eficientes, mas limitados normalmente a ótimos locais, enquanto os métodos híbridos puderam superar estes ótimos locais, utilizando conceitos da metaheurística algoritmo de abelhas para isto. Além disso, pudemos verificar a influência de uma formulação \"forte\" sobre as soluções geradas pelas abordagens de solução, demonstrando que métodos baseados em relaxação linear conseguem obter maiores vantagens deste tipo de formulação, mas outras abordagens podem ou não obter estas vantagens, dependendo do problema abordado / The lot-sizing problem determines a production plan, which supports the decision making, in the medium term, at the industrial environment. This production plan indicates the amounts of each item to be produced in each period of the planning horizon, according to a given objective and satisfying customer\'s demand. Diverse solution methods have been proposed in the literature, considering the difficulty of solving some problem classes and the need of methods to generate solutions quickly. In this work, we develop matheuristics (LP-and-fix, relax-and-fix and fix-and-optimize), one metaheuristic (bees algorithm) and two hybrid methods, used to solve two different multilevel capacitated lot-sizing problems. We also consider the use of three different formulations of the literature to verify the influence of each one on the solutions approaches. The computational results show that the matheuristics proved to be efficient, but usually limited to local optima, while the hybrid methods could escape from these local optima, using concepts of bees algorithm to do this. Additionally, we test the effect of a tight formulation on the solutions approaches, demonstrating that LP-based heuristics can obtain further advantages from this type of formulation, but other approaches can take these advantages, depending on the problem addressed

Quantitative descriptions of reaction kinetics formulated at the stochastic mesoscopic level are frequently used to study various aspects of regulation and control in models of cellular control systems. For this type of systems, numerical simulation offers a variety of challenges caused by the high dimensionality of the problem and the multiscale properties often displayed by the biochemical model. In this thesis I have studied several aspects of stochastic simulation of both well-stirred and spatially heterogenous systems. In the well-stirred case, a hybrid method is proposed that reduces the dimension and stiffness of a model. We also demonstrate how both a high performance implementation and a variance reduction technique based on quasi-Monte Carlo can reduce the computational cost to estimate the probability density of the system. In the spatially dependent case, the use of unstructured, tetrahedral meshes to sample realizations of the stochastic process is proposed. Using such meshes, we then extend the reaction-diffusion framework to incorporate active transport of cellular cargo in a seamless manner. Finally, two multilevel methods for spatial stochastic simulation are considered. One of them is a space-time adaptive method combining exact stochastic, approximate stochastic and macroscopic modeling levels to reduce the simualation cost. The other method blends together mesoscale and microscale simulation methods to locally increase modeling resolution. / eSSENCE

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Ce travail de thèse propose une méthodologie visant la résolution de certains problèmes de classification, notamment ceux concernant la classification séquentielle en tâches de Traitement Automatique des Langues. Afin d'améliorer les résultats de la tâche de classification, nous proposons l'utilisation d'une approche itérative basée sur l'erreur, qui intègre, dans le processus d'apprentissage, des connaissances d'un expert représentées sous la forme de "règles de connaissance". Nous avons appliqué la méthodologie à deux tâches liées à la détection de la spéculation ("hedging") dans la littérature scientifique: la détection de segments textuels spéculatifs ("hedge cue identification") et la détection de la couverture de ces segments ("hedge cue scope detection"). Les résultats son prometteurs: pour la première tâche, nous avons amélioré le F-score de la baseline de 2,5 points en intégrant des données sur la co-occurrence de segments spéculatifs. Concernant la deuxième tâche, l'intégration d'information syntaxique et des règles pour l'élagage syntaxique ont permis d'améliorer les résultats de la classification de 0,712 à 0,835 (F-score). Par rapport aux méthodes de l'état de l'art, les résultats sont très bons et ils suggèrent que l'approche consistant à améliorer les classifieurs basées seulement sur des erreurs commises dans un corpus, peut être également appliquée à d'autres tâches similaires. Qui plus est, ce travail de thèse propose un schéma de classes permettant de représenter l'analyse d'une phrase dans une structure unique qui intègre les résultats de différentes analyses linguistiques. Cela permet de mieux gérer le processus itératif d'amélioration du classifieur, dans lequel différents ensembles d'attributs d'apprentissage sont utilisés à chaque itération. Nous proposons également de stocker les attributs dans un modèle relationnel au lieu des structures textuelles classiques, afin de faciliter l'analyse et la manipulation des données apprises.

En este trabajo se realiza un estudio de varias extensiones del método de las diferencias finitas en el dominio del tiempo (FDTD) que permiten la simulación electromagnética de estructuras híbridas de microondas, incluyendo circuitos activos y pasivos. En primer lugar, se revisan los métodos lumped-element (LE) -FDTD y lumped-network (LN) -FDTD, los cuales permiten la incorporación de circuitos concentrados de dos terminales dentro del formalismo FDTD. En el caso del método LN-FDTD, se realiza también un estudio de sus propiedades numéricas. A continuación se presenta el método two-port (TP) -LN-FDTD, el cual permite incorporar circuitos lineales concentrados de dos puertas en las estructuras híbridas estudiadas. Este método parte de una descripción del cuadripolo en términos de su matriz admitancia expresada en el dominio de Laplace. La discretización se realiza con la ayuda de la técnica de la transformación de Moebius. Por último, una vez validado, este método se combina con otras técnicas para la simulación distintos tipos de circuitos híbridos de microondas. / In this work, a study of several extensions of the conventional finite difference time domain (FDTD) method is been carried out. These extensions enable the electromagnetic simulation of microwave hybrid structures, including passive and active circuits. First, an exhaustive revision of both the lumped-element (LE) -FDTD and the lumped-network (LN) -FDTD methods is performed. These methods allow us to incorporate two-terminal lumped circuits into the FDTD. In addition, the numerical properties of the LN-FDTD method are studied for the first time. Second, the two-port (TP)-LN-FDTD is presented. This method enables the incorporation of linear two-port lumped circuits into the studied hybrid structures. This technique basically consists of describing a TP-LN by means of its admittance matrix in the Laplace domain. Then, by applying the Mobius transformation technique, we obtain the discretized admittance matrix. Finally, this method is combined with other existing techniques to allow the simulation of several microwave hybrid circuits.

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