This dissertation was to study computational theory and methods for ?nding multiple saddle critical points in Banach spaces. Two local minimax methods were developed for this purpose. One was for unconstrained cases and the other was for constrained cases. First, two local minmax characterization of saddle critical points in Banach spaces were established. Based on these two local minmax characterizations, two local minimax algorithms were designed. Their ?ow charts were presented. Then convergence analysis of the algorithms were carried out. Under certain assumptions, a subsequence convergence and a point-to-set convergence were obtained. Furthermore, a relation between the convergence rates of the functional value sequence and corresponding gradient sequence was derived. Techniques to implement the algorithms were discussed. In numerical experiments, those techniques have been successfully implemented to solve for multiple solutions of several quasilinear elliptic boundary value problems and multiple eigenpairs of the well known nonlinear p-Laplacian operator. Numerical solutions were presented by their pro?les for visualization. Several interesting phenomena of the solutions of quasilinear elliptic boundary value problems and the eigenpairs of the p-Laplacian operator have been observed and are open for further investigation. As a generalization of the above results, nonsmooth critical points were considered for locally Lipschitz continuous functionals. A local minmax characterization of nonsmooth saddle critical points was also established. To establish its version in Banach spaces, a new notion, pseudo-generalized-gradient has to be introduced. Based on the characterization, a local minimax algorithm for ?nding multiple nonsmooth saddle critical points was proposed for further study.

We prove some sufficient conditions for obtaining convergence rates in regularization of linear ill-posed problems in a Hilbert space setting and show that these conditions are directly related with the conditional stability in several concrete inverse problems for partial differential equations.

We connect the Mimetic Finite Difference method (MFD) with the finite-volume two-point flux scheme (TPFA) for Voronoi meshes. The main effect is reducing the saddle-point system to a much smaller symmetric-positive definite matrix. In addition, the generalization allows MFD to seamlessly integrate with existing porous media modeling technology. The generalization also imparts the monotonicity property of the TPFA method on MFD. The connection is achieved by altering the consistency condition of the velocity bilinear operator. First-order convergence theory is presented as well as numerical results that support the claims. We demonstrate a methodology for using MFD in modeling fluid flow in fractures coupled with a reservoir. The method can be used for nonplanar fractures. We use the method to demonstrate the effects of fracture curvature on single-phase and multi-phase flows. Standard benchmarks are used to demonstrate the accuracy of the method. The approach is coupled with existing reservoir simulation technology. / text

We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil's response to probing elastic waves. We use the complete waveforms of the medium's response to drive the inverse problem. Specifically, we use a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lame parameters. We discuss strategies that lend algorithmic robustness to the proposed inversion schemes. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). The PML is a buffer zone that surrounds the domain of interest, and enforces the decay of outgoing waves. In order to resolve the forward problem, we present a hybrid finite element approach, where a displacement-stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. We discuss several time-integration schemes, including an explicit Runge-Kutta scheme, which is well-suited for large-scale problems on parallel computers. We report numerical results demonstrating stability and efficacy of the forward wave solver, and also provide examples attesting to the successful reconstruction of the two Lame parameters for both smooth and sharp profiles, using synthetic records. We also report the details of two field experiments, whose records we subsequently used to drive the developed inversion algorithms in order to characterize the sites where the field experiments took place. We contrast the full-waveform-based inverted site profile against a profile obtained using the Spectral-Analysis-of-Surface-Waves (SASW) method, in an attempt to compare our methodology against a widely used concurrent inversion approach. We also compare the inverted profiles, at select locations, with the results of independently performed, invasive, Cone Penetrometer Tests (CPTs). Overall, whether exercised by synthetic or by physical data, the full-waveform inversion method we discuss herein appears quite promising for the robust subsurface imaging of near-surface deposits in support of geotechnical site characterization investigations.

This thesis develops efficient modeling frameworks via a Partial Differential Equation (PDE) approach for multi-factor financial derivatives, with emphasis on three-factor models, and studies highly efficient implementations of the numerical methods on novel high-performance computer architectures, with particular focus on Graphics Processing Units (GPUs) and multi-GPU platforms/clusters of GPUs. Two important classes of multi-factor financial instruments are considered: cross-currency/foreign exchange (FX) interest rate derivatives and multi-asset options. For cross-currency interest rate derivatives, the focus of the thesis is on Power Reverse Dual Currency (PRDC) swaps with three of the most popular exotic features, namely Bermudan cancelability, knockout, and FX Target Redemption. The modeling of PRDC swaps using one-factor Gaussian models for the domestic and foreign interest short rates, and a one-factor skew model for the spot FX rate results in a time-dependent parabolic PDE in three space dimensions. Our proposed PDE pricing framework is based on partitioning the pricing problem into several independent pricing subproblems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Each of these subproblems requires a solution of the model PDE. We then develop a highly efficient GPU-based parallelization of the Alternating Direction Implicit (ADI) timestepping methods for solving the model PDE. To further handle the substantially increased computational requirements due to the exotic features, we extend the pricing procedures to multi-GPU platforms/clusters of GPUs to solve each of these independent subproblems on a separate GPU. Numerical results indicate that the proposed GPU-based parallel numerical methods are highly efficient and provide significant increase in performance over CPU-based methods when pricing PRDC swaps. An analysis of the impact of the FX volatility skew on the price of PRDC swaps is provided. In the second part of the thesis, we develop efficient pricing algorithms for multi-asset options under the Black-Scholes-Merton framework, with strong emphasis on multi-asset American options. Our proposed pricing approach is built upon a combination of (i) a discrete penalty approach for the linear complementarity problem arising due to the free boundary and (ii) a GPU-based parallel ADI Approximate Factorization technique for the solution of the linear algebraic system arising from each penalty iteration. A timestep size selector implemented efficiently on GPUs is used to further increase the efficiency of the methods. We demonstrate the efficiency and accuracy of the proposed GPU-based parallel numerical methods by pricing American options written on three assets.

Simulated moving bed chromatography process (SMBCP) is the technical realisation of a countercurrent adsorption process through the cyclic port switching. SMB technology reduces the cost of packing material with high loading capacity and provides high purity and high recovery in a very short time. Major commodity applications have been found in the petroleum, food, biotechnology, pharmaceutical and fine chemical industries. The industrial applications bring an emergent demand to improve the SMBCP operation for higher product quality, productivity, efficiency and robustness. However, for this particular process, we encounter several challenges. Firstly, the interplay of the effects of strong nonlinearities, competition of solutes, mass transfer resistance and fluid dynamic dispersion produces steep concentration fronts. Mathematical model accounted for this particular property constitutes a serious difficulty for the solution procedure. Secondly, a dynamic SMB model consists of a set of partial differential, ordinary differential and algebraic equations, which are highly coupled. The large size is a problem due to its intensive computation when on-line optimisation and real-time control are necessary. Thirdly, the SMB unit operation exhibits complex dynamics. Process metrics for design and operation can be determined only when a cyclic steady state is reached after a certain number of switching. Achieving this steady state by solving the PDE models cycle after cycle involves expensive calculation. Studies have been carried out to solve these problems through process analysis, investigation on spatial discretisation techniques, and development of an accelerated integration scheme. / Through a systematic study on the advances of SMB modelling, design and control, a set of functionally equivalent models for SMBCP are identified and summarized for their practical applications. The limitations of the existing modelling techniques in industrial applications are also identified. Furthermore, structural analysis of the existing models is conducted for a better understanding of the functionality and suitability of each model. Suggestions are given on how to choose an appropriate model with sufficient accuracy while keeping the computational demand reasonably low for real time control. / Effort is made on to the systematic investigation of different numerical methods for the solution of PDEs to circumvent the steep gradients encountered in chromatographic separation. Comprehensive studies are conducted on a single column chromatographic process represented by a transport-dispersive-equilibrium linear model. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. It reveals that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. / The advantages and disadvantages of the wavelet based approaches are further investigated through several case studies on real SMBCP system. A glucose-fructose separation process is firstly chosen with its relatively simple isotherm representations. Simulations are conducted using both wavelet collocation and upwind finite difference methods. For more complicated applications, an enantiomers separation process is selected. As the PDEs model exhibit a certain degree of singularity, wavelet collocation and high resolution methods are adopted for spatial discretisation. It is revealed that both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. This is the first time that these two frontier numerical methods are used for such a complex SMB system models and our results are encouraging for the development of model-based online control scheme. / In developing a new scheme to rapidly obtain the solution at steady state for any arbitrary initial condition, the concept of Quasi-Envelope (QE) is adopted under the consideration that a SMBCP can be treated as a pseudo-oscillatory process because of a large number of continuous switching. The scheme allows larger steps to be taken to predict the slow change of starting state within each switching. Combined with previously developed wavelet-based technique, this method is successfully applied to the simulation of a SMB sugar separation process. Investigations are also carried out on the location of proper starting point for the algorithm and on the effect of changing stepsize to the convergence of iteration method. It is found that if the starting state of Quasi-Envelope is chosen to be the same as the original function, the multivalue algorithm would require similar computational effort to achieve the steady state prediction, regardless of the integration stepsize. If using constant stepsize, launching QE later is helpful when quasi-envelope displays steep change at the start-up period. A changing stepsize produces slow convergence compared to the constant stepsize strategy, thus increasing the work load where the stepsize change is occurring. Other iteration method is required to be imposed to achieve faster convergence right from the beginning. Potential applications can be seen for other chemical engineering processes with inherent cyclic behaviour.

Cette thèse présente plusieurs contributions méthodologiques au traitement des images multicomposantes. Nous présentons notre travail dans le contexte applicatif difficile de l’imagerie de tomographie d’émission de positons dynamique (TEPd), une modalité d’imagerie fonctionnelle produisant des images multicomposantes fortement dégradées. Le caractère vectoriel du signal offre des propriétés de redondance et de complémentarité de l’information le long des différentes composantes permettant d’en améliorer le traitement. Notre première contribution exploite cet avantage pour la segmentation robuste de volumes d’intérêt au moyen de modèles déformables. Nous proposons un champ de forces extérieures guidant les modèles déformables vers les contours vectoriels des régions à délimiter. Notre seconde contribution porte sur la restauration de telles images pour faciliter leur traitement ultérieur. Nous proposons une nouvelle méthode de restauration par équations aux dérivées partielles permettant d’augmenter le rapport signal sur bruit d’images dégradées et d’en renforcer la netteté. Appliqués à l’imagerie TEPd, nous montrons l’apport de nos contributions pour un problème ouvert des neurosciences, la quantification non invasive d’un radiotraceur de la neuroinflammation. / This thesis presents several methodological contributions to the processing of vector-valued images, with dynamic positron emission tomography imaging (dPET) as its target application. dPET imaging is a functional imaging modality that produces highly degraded images composed of subsequent temporal acquisitions. Vector-valued images often present some level of redundancy or complementarity of information along the channels, allowing the enhancement of processing results. Our first contribution exploits such properties for performing robust segmentation of target volumes with deformable models.We propose a new external force field to guide deformable models toward the vector edges of regions of interest. Our second contribution deals with the restoration of such images to further facilitate their analysis. We propose a new partial differential equation-based approach that enhances the signal to noise ratio of degraded images while sharpening their edges. Applied to dPET imaging, we show to what extent our methodological contributions can help to solve an open problem in neuroscience : noninvasive quantification of neuroinflammation.

In this master thesis, we compare three different types of funding alternatives from a Swedish municipality's point of view, with the main focus on analysing a Nikkei-linked loan. We do this by analysing the resulting interest rate and the expected exposures, taking collateral into consideration. We conclude, with certainty, that there are many alternatives for funding and that they each need to be analysed and compared on many levels to be able to make a correct decision as to which ones to choose. An important part of this is to consider the implications of the newest regulations and risk exposure, as it might greatly influence the final price for contracts. Between the cases that we considered, the SEK bond was the one with the lowest resulting spread, and the one which is the simplest considering the collateral involved. While other alternatives might be better depending on how profitable it is for the municipality to receive collateral, the SEK bond is the most transparent one and with least risk involved.

Made available in DSpace on 2015-05-07T15:08:16Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 724727 bytes, checksum: 7e4fce0ea57137d24d611c0f44e4165b (MD5) Previous issue date: 2011-08-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabajo es un estudio sobre la implementación del plan de desarrollo escolar (PDEescuela) y su impacto en la administración escolar, en las escuelas públicas municipales de João Pessoa/PB. Para este análisis se consideró como límite temporal, el período comprendido entre 1998 y 2006. El PDE-escuela es el principal proyecto del programa Fundo de Fortalecimento da Escola (Fundescola) financiado por el Banco Mundial en colaboración con el Ministerio de educación (MEC). Se trata de una propuesta de planeamiento estratégico que será desarrollado por las escuelas públicas a través de un modelo gerencial. La investigación tuvo como objetivo indagar cómo se dio el proceso de implantación del PDE-escuela en la red pública escolar de João Pessoa en el período 1998-2006 y su contribución en la gestión de estas escuelas. Por tanto, situamos el PDEescuela en el contexto de la reforma del Estado, estudiamos el modelo de gestión gerencial basada en la teoría de la administración moderna y la gestión democrática fundamentada en la participación, autonomía y descentralización. Contamos con las contribuciones teóricas de Abrúcio (1997), Pereira (1998); Dourado (1998; 1999); Libâneo (2001); Fonseca (2003), Cury (2005), Castro (2007), França (2006), Cabral Neto (2009), entre otros. La pesquisa es parte de un enfoque de investigación cualitativa. Elegimos como instrumentos de recopilación de datos, documentos y entrevistas. El análisis de los datos fue hecho a partir de análisis de contenido, utilizando las orientaciones de Bardin (2010). Los resultados indicaron que a pesar del PDE-escuela ser fundamentado en el modelo de gestión gerencial, su implementación contribuyó con la organización del trabajo escolar, la mejoría de las condiciones materiales y pedagógicas, bien como, estimulado la participación de la comunidad en la dinámica de la escuela, contribuyendo así, con a la gestión democrática en las escuelas investigadas. El estudio reveló todavía la necesidad de modificar la estructura del PDE-escuela, teniendo en vista el exceso de burocracia y control, así como, aumentar los valores de los recursos y flexibilizar las reglas para su aplicación y gerenciamiento en el ámbito escolar. / Este trabalho trata de uma pesquisa realizada sobre a implantação do Plano de Desenvolvimento da Escola (PDE-escola) e seu impacto na gestão escolar, nas escolas públicas municipais de João Pessoa/PB. Para esta análise considerou-se como recorte temporal, o período de 1998 a 2006. O PDE-escola é o principal projeto do Programa Fundo de Fortalecimento da Escola (Fundescola) financiado pelo Banco Mundial em parceria com o Ministério da Educação (MEC). Trata-se de uma proposta de planejamento estratégico a ser desenvolvida pelas escolas públicas por meio de um modelo gerencial. A pesquisa objetivou investigar como se deu o processo de implantação do PDE-escola na rede pública escolar de João Pessoa no período de 1998 a 2006 e sua contribuição na gestão dessas escolas. Para tanto, situamos o PDE-escola no contexto da reforma do Estado, estudamos o modelo de gestão gerencial embasado na teoria da administração moderna e a gestão democrática fundada na participação, autonomia e descentralização. Recorremos às contribuições teóricas de Abrúcio (1997), Pereira (1998); Dourado (1998; 1999); Libâneo (2001); Fonseca (2003), Cury (2005), Castro (2007), França (2006), Cabral Neto (2009), entre outros. A investigação insere-se na abordagem qualitativa da pesquisa. Elegemos como instrumentos de coleta de dados, documentos e entrevistas. A análise dos dados foi feita a partir da análise de conteúdo, utilizando-se as orientações de Bardin (2010). Os resultados indicaram que apesar do PDE-escola ser fundamentado no modelo de gestão gerencial, a sua implantação tem contribuído com a organização do trabalho escolar, a melhoria das condições materiais e pedagógicas, bem como, estimulado a participação da comunidade na dinâmica da escola, contribuindo, assim, com a gestão democrática nas escolas pesquisadas. O estudo revelou, ainda, a necessidade de modificar a estrutura do PDE-escola, tendo em vista o excesso de burocracia e controle, bem como, aumentar os valores dos recursos e flexibilizar as regras para a sua aplicação e gerencia no âmbito escolar.

Em decorrência ao grande crescimento e evolução dos processos de usinagem e a demanda para adequação ambiental, novos fluidos de corte tem sido aplicados. Uma comprovação de sua eficiência em refrigerar a peça, e a ferramenta melhorando a produtividade do processo ainda é necessária. O presente trabalho propõe o estudo e o desenvolvimento de um sistema para avaliar a eficácia de fluidos de corte em operações de usinagem. Inicia-se com uma abordagem matemática da modelagem do processo de dissipação de calor em operações de usinagem. Em seguida prossegue-se com uma investigação de diferentes maneiras de solução do modelo proposto. Experimentos práticos foram realizados no laboratório de Otimização de Processos de Fabricação - OPF. A partir dos dados obtidos foi realizada uma análise assintótica das equações diferencias parciais que governam o modelo. Finalizando, o modelo selecionado foi aplicado no fresamento do aço AISI 4340 endurecido usinado sob alta velocidade. / Due to the rapid growth and development of machining processes there has been a demand for environmental sustainability and news cutting fluids have been applied. A reliable assessment of their efficiency in cooling the workpiece, tools and improving productivity is still a requirement. The present thesis presents a theoretical study and a proposal of a system to assess the effectiveness of cutting fluids applied to machining operation. It begins using a mathematical approach to model the heat propagation during machining operations. Then, it continues with an investigation into different ways to solve the proposed theorical model. Machining experiments using realistic cutting operations were also conducted at the Laboratory for Optimization of Manufacturing Processes - OPF. From the experimental data, was carried out an asymptotic analysis of partial differential equations, which govern the mathematical model. Finally, the selected model will be applied to a milling operation using High Speed Machining (HSM) technique on hardened steel AISI 4340.