In this dissertation, a Method of Moments (MoM) Volume Integral Equation (VIE)-based modeling approach suitable for a patch or slot antenna on a thin finite dielectric substrate is developed and validated. Two new key features of this method are the use of proper dielectric basis functions and proper VIE conditioning, close to the metal surface, where the surface boundary condition of the zero tangential-component must be extended into adjacent tetrahedra. The extended boundary condition is the exact result for the piecewise-constant dielectric basis functions. The latter operation allows one to achieve a good accuracy with one layer of tetrahedra for a thin dielectric substrate and thereby greatly reduces computational cost. The use of low-order basis functions also implies the use of low-order integration schemes and faster filling of the impedance matrix. For some common patch/slot antennas, the VIE-based modeling approach is found to give an error of about 1% or less in the resonant frequency for one-layer tetrahedral meshes with a relatively small number of unknowns. This error is obtained by comparison with fine finite- element method (FEM) simulations, or with measurements, or with the analytical mode matching approach. Hence it is competitive with both the method of moments surface integral equation approach and with the FEM approach for the printed antennas on thin dielectric substrates. Along with the MoM development, the dissertation also presents the models and design procedures for a number of practical antenna configurations. They in particular include: i. a compact linearly polarized broadband planar inverted-F antenna (PIFA); ii. a circularly polarized turnstile bowtie antenna. Both the antennas are designed to operate in the low UHF band and used for indoor positioning/indoor geolocation.

Made available in DSpace on 2016-12-23T14:08:09Z (GMT). No. of bitstreams: 1 Parte Inicial.pdf: 580643 bytes, checksum: 1783483d80317ac5307ad55e7cbdb752 (MD5) Previous issue date: 2013-03-25 / O propósito da pesquisa aqui elaborada é mostrar a viabilidade da aplicação de Funções de Base Radial de Suporte Compacto (FBRSC) no processo de aproximação direta do núcleo da ação de domínio através de integração de contorno. Essa formulação utilizada no tratamento da integral de domínio é denominada como (Método dos Elementos de Contorno com Integração Direta de Contorno) MECIC. Com o intuito de se avaliar a efetividade das FBRSC como funções de interpolação, serão realizados diversos testes numéricos, onde se deseja calcular o volume de superfícies. Então, serão realizados testes bidimensionais de aproximação, variando-se o suporte das FBRSCs, a fim de analisar o comportamento dessas funções. Depois de verificar a efetividade e a precisão das FBRSCs no processo de interpolação, desenvolvem-se programas, no ambiente do Método dos Elementos de Contorno (MEC), para a solução de problemas governados pela Equação de Poisson com a Formulação MECIC associada ao conceito de interpolação com FBRSC com suporte devidamente otimizados. A aferição das soluções numéricas obtidas se dá a partir da comparação com as suas respectivas soluções analíticas, facilmente encontradas na literatura especializada. Assim, possibilita-se estimar o erro relativo e então a eficácia da Formulação MECIC com FBRSC. Uma vez comprovado a sua eficácia, a Formulação MECIC com FBRSC é testada também com o esquema de interpolação com ajuste de pontos. Durante todo o desenvolvimento, atenta-se para a importância do custo computacional da formulação, a partir da geração de tabelas com o tempo de processamento dos programas implementados no MEC. Dessa forma, avalia-se qualitativamente o desempenho das FBRSC na Formulação MECIC, visando futuras aplicações na área de propagação de ondas sísmicas / The purpose of this research is to show the viability of application of Compactly Supported Radial Basis Function (CSRBF) in the process of direct approximation of the core of the domain action through boundary integration. This formulation is termed as (Boundary Elements Method with Directs Boundary Integration) MECIC, and is used in the treatment of the domain integration. By evaluating the effectiveness of CSRBF as interpolation functions, it performed several numerical tests to calculate the volume of surfaces. Also; by varying the support of CSRBFs, it performed two-dimensional approximation tests to examine the behavior of these functions. After verifying the effectiveness and accuracy of CSRBFs in the interpolation process, it developed computational programs to solve physical problems using the MECIC formulation, which is governed by Poisson s Equation. That formulation is associated with the concept of CSRBF in which the support is properly optimized. The calibration of the numerical solutions is given by the confrontation with their respective analytical solutions, easily found in the specialized literature. In this way, it is possible to estimate the relative error and the effectiveness of the MECIC formulation in association with the CSRBF concept. It is tested also with the curve fitting interpolation scheme. Owing the importance of the computational cost of that formulation, it is generated several time tables showing the processing time of those Boundary Elements Method computational programs. Therefore; aiming future applications in the seismic propagation wave area, it was finally evaluated the qualitative performance of the CSRBF in MECIC s formulation

在許多的研究和應用之中都需要預測的技巧。本論文中, 我們建構了一個 新的神經網路模式--動態徑向基底函數 (dynamical radial basis function) 網路 (DRBF網路) , 並且用這種模式的神經網路作為「函數近 似子」(function approximator) 去處理預測上的問題。另外我們也設計 幾種不同的學習演算法以測試DRBF網路的功能。 / The forecasting technique is important for many researches and applications. In this paper, we shall construct a new model of neural networks -- the dynamical radial basis function (DRBF) networks and use the DRBF networks as "function approximators" to solve some forecasting problems. Different learning algorithms are used to test the capability of DRBF networks.

Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial products exists in the market, such as forwards, futures, swaps and options. Our main focus in this thesis is to use the numerical analysis tools to solve some option pricing problems. Depending upon the inter-relationship of the financial derivatives, the dimension of the associated problem increases drastically and hence conventional methods (for example, the finite difference methods or finite element methods) for solving them do not provide satisfactory results. To resolve this issue, we use a special class of numerical methods, namely, the mesh free methods. These methods are often better suited to cope with changes in the geometry of the domain of interest than classical discretization techniques. In this thesis, we apply these methods to solve problems that price standard and non-standard options. We then extend the proposed approach to solve Heston' volatility model. The methods in each of these cases are analyzed for stability and thorough comparative numerical results are provided.

Environmental simulation models have been playing a key role in civil and environmental engineering decision making processes for decades. The utility of an environmental model depends on how well the model is structured and calibrated. Model calibration is typically in an automated form where the simulation model is linked to a search mechanism (e.g., an optimization algorithm) such that the search mechanism iteratively generates many parameter sets (e.g., thousands of parameter sets) and evaluates them through running the model in an attempt to minimize differences between observed data and corresponding model outputs. The challenge rises when the environmental model is computationally intensive to run (with run-times of minutes to hours, for example) as then any automatic calibration attempt would impose a large computational burden. Such a challenge may make the model users accept sub-optimal solutions and not achieve the best model performance. The objective of this thesis is to develop innovative strategies to circumvent the computational burden associated with automatic calibration of computationally intensive environmental models. The first main contribution of this thesis is developing a strategy called “deterministic model preemption” which opportunistically evades unnecessary model evaluations in the course of a calibration experiment and can save a significant portion of the computational budget (even as much as 90% in some cases). Model preemption monitors the intermediate simulation results while the model is running and terminates (i.e., pre-empts) the simulation early if it recognizes that further running the model would not guide the search mechanism. This strategy is applicable to a range of automatic calibration algorithms (i.e., search mechanisms) and is deterministic in that it leads to exactly the same calibration results as when preemption is not applied. One other main contribution of this thesis is developing and utilizing the concept of “surrogate data” which is basically a reasonably small but representative proportion of a full set of calibration data. This concept is inspired by the existing surrogate modelling strategies where a surrogate model (also called a metamodel) is developed and utilized as a fast-to-run substitute of an original computationally intensive model. A framework is developed to efficiently calibrate hydrologic models to the full set of calibration data while running the original model only on surrogate data for the majority of candidate parameter sets, a strategy which leads to considerable computational saving. To this end, mapping relationships are developed to approximate the model performance on the full data based on the model performance on surrogate data. This framework can be applicable to the calibration of any environmental model where appropriate surrogate data and mapping relationships can be identified. As another main contribution, this thesis critically reviews and evaluates the large body of literature on surrogate modelling strategies from various disciplines as they are the most commonly used methods to relieve the computational burden associated with computationally intensive simulation models. To reliably evaluate these strategies, a comparative assessment and benchmarking framework is developed which presents a clear computational budget dependent definition for the success/failure of surrogate modelling strategies. Two large families of surrogate modelling strategies are critically scrutinized and evaluated: “response surface surrogate” modelling which involves statistical or data–driven function approximation techniques (e.g., kriging, radial basis functions, and neural networks) and “lower-fidelity physically-based surrogate” modelling strategies which develop and utilize simplified models of the original system (e.g., a groundwater model with a coarse mesh). This thesis raises fundamental concerns about response surface surrogate modelling and demonstrates that, although they might be less efficient, lower-fidelity physically-based surrogates are generally more reliable as they to-some-extent preserve the physics involved in the original model. Five different surface water and groundwater models are used across this thesis to test the performance of the developed strategies and elaborate the discussions. However, the strategies developed are typically simulation-model-independent and can be applied to the calibration of any computationally intensive simulation model that has the required characteristics. This thesis leaves the reader with a suite of strategies for efficient calibration of computationally intensive environmental models while providing some guidance on how to select, implement, and evaluate the appropriate strategy for a given environmental model calibration problem.

In this paper an overview is given on the application of directional basis functions, known under the name Curvelets/Contourlets, to various aspects of seismic processing and imaging. Key concepts in the approach are the use of (i) that localize in both domains (e.g. space and angle); (ii) non-linear estimation, which corresponds to localized muting on the coefficients, possibly supplemented by constrained optimization (iii) invariance of the basis functions under the imaging operators. We will discuss applications that include multiple and ground roll removal; sparseness-constrained least-squares migration and the computation of 4-D difference cubes.

En synthèse d'images, le principal calcul à effectuer pour générer une image a été formalisé dans une équation appelée équation du rendu [Kajiya1986]. Cette équation est la intègre la conservation de l'\'energie dans le transport de la lumi\`ere. Elle stipule que l'énergie lumineuse renvoyée, par les objets d'une scène, dans une direction donnée est égale à la somme de l'énergie émise et réfléchie par ceux-ci. De plus, l'énergie réfléchie par un élément de surface est définie comme la convolution de l'éclairement incident avec une fonction de réflectance. Cette dernière modélise le matériau (au sens physique) de l'objet et joue le rôle d'un filtre directionnel et énergétique dans l'équation du rendu, simulant ainsi la manière dont la surface se comporte vis-à-vis d'une réflexion. Dans ce mémoire de thèse, nous introduisons de nouvelles représentations pour la fonction de réflectance ainsi que pour la représentation de l'éclairement incident. Dans la première partie de ce mémoire, nous proposons deux nouveaux modèles pour représenter la fonction de réflectance. Le premier modèle s'inscrit dans une démarche artistique et est destiné à faciliter la création et l'édition des reflets spéculaires. Son principe est de laisser l'utilisateur peindre et esquisser les caractéristiques (forme, couleur, gradient et texture) du reflet spéculaire dans un plan de dessin paramétrisé en fonction de la direction de la réflexion miroir de la lumière. Le but du second modèle est de représenter de manière compacte et efficace les mesures des matériaux isotropes. Pour ce faire, nous introduisons une nouvelle représentation à base de polynômes rationnels. Les coefficients de ces derniers sont obtenus à l'aide d'un processus d'approximation qui garantit une solution optimale au sens de la convergence. Dans la seconde partie de ce mémoire, nous introduisons une nouvelle représentation volumétrique pour l'éclairement indirect représenté directionnellement à l'aide de vecteurs d'irradiance. Nous montrons que notre représentation est compacte et robuste aux variations géométriques et qu'elle peut être utilisée comme système de cache pour du rendu temps réel ou non, ainsi que dans le cadre de la transmission progressive des données (streaming). Enfin, nous proposons deux types de modifications de l'éclairement incident afin de mettre en valeur les détails et les formes d'une surface. Le première modification consiste à perturber les directions de l'éclairement incident tandis que la seconde consiste à en modifier l'intensité. / In image synthesis, the main computation involved to generate an image is characterized by an equation named rendering equation [Kajiya1986]. This equation represents the law of energy conservation. It stipulates that the light emanating from the scene objects is the sum of the emitted energy and the reflected energy. Moreover, the reflected energy at a surface point is defined as the convolution of the incoming lighting with a reflectance function. The reflectance function models the object material and represents, in the rendering equation, a directional and energetic filter that describes the surface behavior regarding the reflection. In this thesis, we introduce new representations for the reflectance function and the incoming lighting. In the first part of this thesis, we propose two new models for the reflectance function. The first model is targeted for artists to help them create and edit highlights. Our main idea is to let the user paint and sketch highlight characteristics (shape, color, gradient and texture) in a plane parametrized by the incident lighting direction. The second model is designed to represent efficiently isotropic material data. To achieve this result, we introduce a new representation of the reflectance function that uses rational polynomials. Their coefficients are computed using a fitting process that guarantees an optimal solution regarding convergence. In the second part of this thesis, we introduce a new volumetric structure for indirect illumination that is directionally represented with irradiance vector. We show that our representation is compact and robust to geometric variations, that it can be used as caching system for interactive and offline rendering and that it can also be transmitted with streaming techniques. Finally, we introduce two modifications of the incoming lighting to improve the shape depiction of a surface. The first modification consists in warping the incoming light directions whereas the second one consists in scaling the intensity of each light source. / Réalisé en cotutelle avec l'Université Bordeaux 1 (France)

Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial products exists in the market, such as forwards, futures, swaps and options. Our main focus in this thesis is to use the numerical analysis tools to solve some option pricing problems. Depending upon the inter-relationship of the financial derivatives, the dimension of the associated problem increases drastically and hence conventional methods (for example, the finite difference methods or finite element methods) for solving them do not provide satisfactory results. To resolve this issue, we use a special class of numerical methods, namely, the mesh free methods. These methods are often better suited to cope with changes in the geometry of the domain of interest than classical discretization techniques. In this thesis, we apply these methods to solve problems that price standard and non-standard options. We then extend the proposed approach to solve Heston' volatility model. The methods in each of these cases are analyzed for stability and thorough comparative numerical results are provided.

This thesis describes theory and algorithms for use with Radial Basis Functions (RBFs), emphasising techniques motivated by three particular application areas. In Part I, we apply RBFs to the problem of interpolating to integral data. While the potential of using RBFs for this purpose has been established in an abstract theoretical context, their use has been lacking an easy to check sufficient condition for finding appropriate parent basic functions, and explicit methods for deriving integral basic functions from them. We present both these components here, as well as explicit formulations for line segments in two dimensions and balls in three and five dimensions. We also apply these results to real-world track data. In Part II, we apply Hermite and pointwise RBFs to the problem of surface reconstruction. RBFs are used for this purpose by representing the surface implicitly as the zero level set of a function in 3D space. We develop a multilevel piecewise technique based on scattered spherical subdomains, which requires the creation of algorithms for constructing sphere coverings with desirable properties and for blending smoothly between levels. The surface reconstruction method we develop scales very well to large datasets and is very amenable to parallelisation, while retaining global-approximation-like features such as hole filling. Our serial implementation can build an implicit surface representation which interpolates at over 42 million points in around 45 minutes. In Part III, we apply RBFs to the problem of animation control in the area of motion synthesis---controlling an animated character whose motion is entirely the result of simulated physics. While the simulation is quite well understood, controlling the character by means of forces produced by virtual actuators or muscles remains a very difficult challenge. Here, we investigate the possibility of speeding up the optimisation process underlying most animation control methods by approximating the physics simulator with RBFs.

Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances. When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries. Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation. In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme. The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.