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Hudson, Justin. "Numerical techniques for morphodynamic modelling". Thesis, University of Reading, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.394022.
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Djambazov, Georgi Stefanov. "Numerical techniques for computational aeroacoustics". Thesis, University of Greenwich, 1998. http://gala.gre.ac.uk/6149/.
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The problem of aerodynamic noise is considered following the Computational Aeroacoustics approach which is based on direct numerical simulation of the sound field. In the region of sound generation, the unsteady airflow is computed separately from the sound using Computational Fluid Dynamics (CFD) codes. Overlapping this region and extending further away is the acoustic domain where the linearised Euler equations governing the sound propagation in moving medium are solved numerically. After considering a finite volume technique of improved accuracy, preference is given to an optimised higher order finite difference scheme which is validated against analytical solutions of the governing equations. A coupling technique of two different CFD codes with the acoustic solver is demonstrated to capture the mechanism of sound generation by vortices hitting solid objects in the flow. Sub-grid turbulence and its effect 011sound generation has not been considered in this thesis. The contribution made to the knowledge of Computational Aeroacoustics can be summarised in the following: 1) Extending the order of accuracy of the staggered leap-frog method for the linearised Euler equations in both finite volume and finite difference formulations; 2) Heuristically determined optimal coefficients for the staggered dispersion relation preserving scheme; 3) A solution procedure for the linearised Euler equations involving mirroring at solid boundaries which combines the flexibility of the finite volume method with the higher accuracy of the finite difference schemes; 4) A method for identifying the sound sources in the CFD solution at solid walls and an expansion technique for sound sources inside the flow; 5) Better understanding of the three-level structure of the motions in air: mean flow, flow perturbations, and acoustic waves. It can be used, together with detailed simulation results, in the search for ways of reducing the aerodynamic noise generated by propellers, jets, wind turbines, tunnel exits, and wind-streamed buildings.
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Fraser-Andrews, G. "Numerical techniques for singular optimal trajectories". Thesis, University of Hertfordshire, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372080.
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The objectives of the subject-matter of this thesis were to appraise some methods of solving non-singular optimal control problems by their degree of success in tackling four chosen problems and then to try the most promising methods on chosen singular problems. In Part I of this thesis, the chosen problems are attempted by quasilinearisation, two versions of shooting, Miels's method, differential dynamic programming and two versions of parameterisation . Conclusions on the various methods are given. NOC shooting, developed by the Numerical Optimisation Centre of The Hatfield Polytechnic, and constrained optimisation were found to be very useful for non-singular problems. In Part 11, the properties and calculation of possible singular controls are investigated, then the two chosen methods used. It was found that NOC shooting was again very useful, provided the solution structure is known and that constrained parameterisation was invaluable for determining the solution structure and when shooting is impossible. Contributions to knowledge as as follows. In Part I, the relative merits of various methods are displayed, additions are made to the theory of parameterisation, shooting and quasilinearisation, the best solutions known of the chosen problems are produced and choices of optimisation parameters for one chosen problem, the satellite problem, are compared. The satellite problem has dependent state variables and the Maximum Principle is extended in Appendix III to cover this case . In Part II, a thorough survey of the properties of singular controls is given, the calculation of possible singular controls clarified and extended, the utility of the two chosen methods is displayed, the best solutions known of the Goddard problem obtained with improved understanding of transitions in soluti on structures , Cl problem studied with control dependent on the costate variables and singular solution structures found.
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Hyde, Paul. "Numerical techniques for optimising rail grinding". Thesis, University of Newcastle upon Tyne, 2012. http://hdl.handle.net/10443/1468.
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Grinding of rails is a technique widely used within the railway industry to balance the degradation of the condition of the rail with the required performance of the rail. The principal focus of this research is the impact of wear and rolling contact fatigue (RCF) cracks on structural integrity of rails, and how rail grinding affects this relationship. A numerical model which predicts growth of RCF-initiated cracks in rails has been adapted to take into account periodic grinding of the surface of the rail. The suitability of some of the simplifying assumptions of the adapted model, referred to as the Grinding Model, has been examined with a physical test program, using full scale rail vehicles and track. This test program studied the persistence of the characteristic surface roughness of the rail generated by grinding, and was carried out to determine whether the effect of this roughness on crack growth can be neglected in the Grinding Model. The Grinding Model has been used to predict crack size, in order to investigate the effect of different grinding strategies, consisting of a depth of grinding applied at a certain interval during a representative pattern of rail vehicle traffic over the rail. The use of the Grinding Model to find grinding strategies which match an optimum criterion has been demonstrated. The applicability of this optimisation technique and the model in its current state of development, to the specification of rail grinding operations, in the context of maximising safe rail life and minimising rail life cycle cost, is discussed.
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O'Sullivan, E. A. "Numerical noise reduction techniques in signal processing". Thesis, Queen's University Belfast, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426583.
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Mvondo, Bernardin Gael. "Numerical techniques for optimal investment consumption models". University of the Western Cape, 2014. http://hdl.handle.net/11394/4352.
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>Magister Scientiae - MScThe problem of optimal investment has been extensively studied by numerous researchers in order to generalize the original framework. Those generalizations have been made in different directions and using different techniques. For example, Perera [Optimal consumption, investment and insurance with insurable risk for an investor in a Levy market, Insurance: Mathematics and Economics, 46 (3) (2010) 479-484] applied the martingale approach to obtain a closed form solution for the optimal investment, consumption and insurance strategies of an individual in the presence of an insurable risk when the insurable risk and risky asset returns are described by Levy processes and the utility is a constant absolute risk aversion. In another work, Sattinger [The Markov consumption problem, Journal of Mathematical Economics, 47 (4-5) (2011) 409-416] gave a model of consumption behavior under uncertainty as the solution to a continuous-time dynamic control problem in which an individual moves between employment and unemployment according to a Markov process. In this thesis, we will review the consumption models in the above framework and will simulate some of them using an infinite series expansion method − a key focus of this research. Several numerical results obtained by using MATLAB are presented with detailed explanations.
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Kawabata, Hideyuki. "Compiler techniques for large-scale numerical computations". 京都大学 (Kyoto University), 2004. http://hdl.handle.net/2433/145358.
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Scott, Michael Andrew. "Interior node projection techniques in sweeping algorithms /". Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1121.pdf.
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Peter, Felix. "A quantitative comparison of numerical option pricing techniques". St. Gallen, 2008. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/01592823001/$FILE/01592823001.pdf.
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Balcázar, Arciniega Néstor Vinicio. "Numerical simulation of multiphase flows : level-set techniques". Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/279386.
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This thesis aims at developing numerical methods based on level-set techniques suitable for the direct numerical simulation (DNS) of free surface and interfacial flows, in order to be used on basic research and industrial applications.
First, the conservative level-set method for capturing the interface between two fluids is combined with a variable density projection scheme in order to simulate incompressible two-phase flows on unstructured meshes. All equations are discretized by using a finite-volume approximation on a collocated grid arrangement. A high order scheme based on a flux limiter formulation, is adopted for approximating the convective terms, while the diffusive fluxes are centrally differenced. Gradients are computed by the least-squares approach, whereas physical properties are assumed to vary smoothly in a narrow band around the interface to avoid numerical instabilities. Surface tension force is calculated according to the continuous surface force approach. The numerical method is validated against experimental and numerical data reported in the scientific literature.
Second, the conservative level-set method is applied to study the gravity-driven bubbly flow. Unlike the cases presented in the first part, a periodic boundary condition is applied in the vertical direction, in order to mimic a channel of infinite length. The shape and terminal velocity of a single bubble which rises in a quiescent liquid are calculated and validated against experimental results reported in the literature. In addition, different initial arrangements of bubble pairs were considered to study its hydrodynamic interaction, and, finally the interaction of multiple bubbles is explored in a periodic vertical duct, allowing their coalescence.
In the third part of this thesis, a new methodology is presented for simulation of surface-tension-driven interfacial flows by combining volume-of-fluid with level-set methods. The main idea is to benefit from the advantage of each strategy, which is to minimize mass loss through the volume-of-fluid method, and to keep a fine description of the interface curvature using a level-set function. With the information of the interface given by the volume-of-fluid method, a signed distance function is reconstructed following an iterative geometric algorithm, which is used to compute surface tension force. This numerical method is validated on 2D and 3D test cases well known in the scientific literature. The simulations reveal that numerical schemes afford qualitatively similar results to those obtained by the conservative level-set method. Mass conservation is shown to be excellent, while geometrical accuracy remains satisfactory even for the most complex cases involving topology changes.
In the fourth part of the thesis a novel multiple marker level-set method is presented.
This method is deployed to perform numerical simulation of deformable fluid particles without numerical coalescence of their interfaces, which is a problem inherent to standard interface tracking methodologies (e.g. level-set and volume of fluid). Each fluid particle is described by a separate level-set function, thus, different interfaces can be solved in the same control volume, avoiding artificial and potentially unphysical coalescence of fluid particles. Therefore, bubbles or droplets are able to approach each other closely, within the size of one grid cell, and can even collide.
The proposed algorithm is developed in the context of the conservative levelset method, whereas, surface tension is modeled by the continuous surface force approach. The pressure-velocity coupling is solved by the fractional-step projection method. For validation of the proposed numerical method, the gravity-driven impact of a droplet on a liquid-liquid interface is studied; then, the binary droplet collision with bouncing outcome is examined, and finally, it is applied on simulation of gravity-driven bubbly flow in a vertical column. The study of these cases contributed to shed some light into physics present in bubble and droplet flows.Ésta tesis se enfoca en el desarrollo de métodos numéricos basados en la aplicación de técnicas level-set para la Simulación Numérica Directa (DNS) de flujos interfaciales y flujos de superficie libre, con el objetivo de ser usados tanto en investigación básica como en aplicaciones industriales. Primero, el método level-set conservativo desarrollado para la captura de interfaces entre dos fluidos, es combinado con un esquema de proyección adaptado para un fluido de densidad variable, con el objetivo de simular flujos de dos fases en mallas no estructuradas. Todas las ecuaciones son discretizadas mediante una aproximación de volúmenes finitos sobre un arreglo de malla colocada. Un esquema de alto orden cuya formulación se basa en el uso de limitadores de flujo, es usado para la discretización de los términos convectivos, mientras que los flujos difusivos son calculados mediante diferencias centradas. Los gradientes son calculados mediante el método de los mínimos cuadrados, en tanto que se asume que las propiedades físicas varían suavemente en una zona estrecha alrededor de la interface con el objetivo de evitar inestabilidades numéricas. La tensión superficial es incorporada mediante el enfoque de la fuerza superficial continua. El método numérico es validado con respecto a los datos experimentales y numéricos reportados en la literatura científica. Segundo, el método level-set conservativo es aplicado en el estudio del flujo de burbujas conducidas por la gravedad. A diferencia de los casos precedentes, se aplica una condición de frontera periódica en la dirección vertical, con el objetivo de simular un canal de longitud infinita. La forma y velocidad terminal de una burbuja ascenciendo en un líquido inicialmente en reposo son calculadas y contrastadas con los resultados reportados en la literatura. Adicionalmente se estudia la interacción hidrodinámica de un par de burbujas para diferentes configuraciones, y finalmente se explora la interacción de un emjambre de burbujas ascendiendo en un canal vertical. En la tercera parte de ésta tesis, se presenta una nueva metodología para la simulación de flujos interfaciales conducidos por la tensión superficial, mediante la combinación de los métodos volume-of-fluid y level-set. La idea principal se basa en usar el método volume-of-fluid para advectar la interface, minimizando las pérdidas de masa, mientras que las propiedades geométricas de la interface se calculan a partir de una función level-set obtenida mediante un algoritmo geométrico iterativo. La propiedades geométricas así calculadas son usadas para el cómputo de la tensión superficial. El método numérico es validado mediante casos bi y tri-dimensionales bien conocidos en la literatura científica. La conservación de la masa es excelente en tanto que la precisión del método es altamente satisfactoria incluso en los casos más complejos. En la cuarta parte de ésta tesis se presenta un nuevo método level-set de múltiples marcadores. Éste método es diseñado para llevar a cabo simulaciones numéricas de partículas de fluido deformables, evitando la coalescencia numérica de las interfaces. Cada partícula de fluido es capturada por una función level-set distinta, así, diferentes interfaces pueden ser resueltas en el mismo volumen de control, evitando la coalescencia artificial y potencialmente no-física de las partículas fluidas. Por lo tanto, las burbujas (o gotas) pueden acercarce y colisionar. El algoritmo es propuesto en el contexto del método level-set conservativo, mientras que la tensión superficial se resuelve mediante una adaptación del enfoque de la fuerza superficial continua. Para su validación, se estudia el impacto conducido por la gravedad de una gota sobre una interface líquido-líquido; luego, se estudia la collisión de dos gotas con salida rebotante, y finalmente el método numérico es aplicado para la simulación de un enjambre de burbujas sin coalescencia numérica.
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Ortega, Gelabert Olga. "Advanced numerical techniques for inverse problems in geophysics". Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/670631.
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This thesis presents an efficient methodology to couple Model Order Reduction techniques within the framework of geophysical probabilistic inversion problems. Accurate models of the interaction between Earth inner processes and surface features are essential to make reliable predictions of the observables which are a fundamental part of Bayesian inference. Markov Chain Monte Carlo (MCMC) methods have become standard in dealing with probabilistic inversions and they rely on sampling strategies that require solving forward problems many times. Computationally expensive large-scale forward problems are the principal bottleneck that can limit the capabilities and potential of multi-observable geophysical probabilistic inversions. In particular, dynamical effects arising from the sub-lithospheric mantle flow are not usually taken into account in the estimation of surface elevation due to the high computational cost of the associated 3D Stokes flow problem.
The main idea of this thesis is to use the Reduced Basis (RB) method as a surrogate of the true forward problem (3D Stokes flow) to provide fast and accurate approximations. The surrogate is then used to generate samples of the posterior distribution at a much lower computational cost. RB strategies are based on expressing the solution of a problem in a low dimensional space, i.e. a reduced basis. Taking advantage of the convergence nature of the MCMC, we propose a greedy strategy that builds the reduced basis on the fly and as required by the inverse problem. In doing so, the basis is specifically tailored to the posterior features of the problem. In addition, to guarantee an accurate surrogate we define a goal-oriented error estimator which focuses on a particular Quantity of Interest of the problem and, therefore, it guides the basis to achieve the required accuracy in such particular features. All this translates into a problem-shaped basis that is more compact and smaller than if it had to be accurate everywhere in the domain. Moreover, to deal with the costly assembly of matrices, we use the specific parametrization of the problem and sampling strategy to define an assembly procedure that efficiently updates the matrices only with the contribution of the elements that changed between successive inversion steps.
The benefits and limitations of the method are illustrated through several numerical examples. Finally, to demonstrate the applicability of the method two more realistic inverse problems are presented. The first one uses dynamic topography to infer the Lithosphere-Asthenosphere Boundary depth of a spherical domain representing a portion of Earth and the second one is applied to a larger problem in which the African lithospheric structure is discretized in 1225 inversion parameters.Aquesta tesi introdueix una metodologia eficient per acoblar tècniques de Reducció d’Ordre del Model dins el marc de problemes d’inversió probabilística en geofísica. Disposar de models precisos sobre la interacció entre els processos interns de la Terra i les característiques superficials és essencial per tal de fer prediccions fiables dels observables, ja que aquests són una part fonamental de la inferència Bayesiana. Els mètodes de Markov Chain Monte Carlo (MCMC) s’han convertit en un estàndard per tractar amb inversions probabilístiques i es basen en estratègies de mostreig que requereixen solucionar molts problemes directes moltes vegades. L’elevat cost computacional dels problemes directes a gran escala és el principal coll d’ampolla que pot limitar les capacitats i potencial de les inversions probabilístiques multi-observables en geofísica. En concret, els efectes dinàmics provinents del flux del mantell sub-litosfèric no es solen tenir en compte per a l’estimació de l’elevació de la superfície degut a l’elevat cost computacional derivat de resoldre el problema associat de flux de Stokes en 3D. La idea principal d’aquesta tesi es fer servir el mètode de la Base Reduida (RB) com a substitut del problema directe real (flux 3D Stokes) per tal d’obtenir aproximacions ràpides i precises. El substitut es fa servir per generar mostres de la distribució posterior amb un cost computacional molt inferior. Les estratègies RB es basen en expressar la solució d’un problema en un espai de baixa dimensió, i.e. una base reduïda. Aprofitant la naturalesa convergent del MCMC, proposem una estratègia “greedy” que construeix la base sobre la marxa i segons ho requereixi el problema invers. D’aquesta forma, la base està feta a mida per adaptar-se a les característiques posteriors del problema. A més, per tal de garantir la precisió del substitut, definim un estimador d’error “goal-oriented” que es centra en una Quantitat d’Interès específica del problema i, per tant, guia a la base per tal d’aconseguir la precisió necessària en aquelles característiques en particular. Tot això es tradueix en una base adaptada al problema que es més compacta i petita que si hagués de ser precisa en tot el domini. A més, per tal d’afrontar el car assemblatge de les matrius, utilitzem la parametrització del problema i l’estratègia de mostreig per definir una estratègia d’assemblatge que actualitza eficientment les matrius només amb la contribució d’aquells elements que han canviat entre passos successius de la inversió. Els beneficis i limitacions del mètode s’il·lustren a traves de varis exemples numèrics. Finalment, per demostrar l’aplicabilitat del mètode, es presenten dues inversions de problemes més realistes. El primer fa servir la topografia dinàmica per a obtenir la profunditat del límit Litosfera-Astenosfera en un domini esfèric que representa una part de la Terra i el segon s’aplica a un problema més gran en que l’estructura litosfèrica d’Àfrica està discretitzada en 1225 paràmetres.
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Marmie, John A. "Modern numerical electromagnetic techniques applied to aviation problems". Ohio : Ohio University, 1989. http://www.ohiolink.edu/etd/view.cgi?ohiou1182443521.
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Deo, H. S. "Numerical techniques for predicting aerodynamic characteristics of bodies". Thesis, Cranfield University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371828.
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Fairbanks, James Paul. "Graph analysis combining numerical, statistical, and streaming techniques". Diss., Georgia Institute of Technology, 2016. http://hdl.handle.net/1853/54972.
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Graph analysis uses graph data collected on a physical, biological, or social
phenomena to shed light on the underlying dynamics and behavior of the agents in that system. Many fields contribute to this topic including graph theory, algorithms, statistics, machine learning, and linear algebra. This dissertation advances a novel framework for dynamic graph analysis that combines numerical, statistical, and streaming algorithms to provide deep
understanding into evolving networks. For example, one can be interested in the changing influence structure over time. These disparate techniques each
contribute a fragment to understanding the graph; however, their combination
allows us to understand dynamic behavior and graph structure. Spectral partitioning methods rely on eigenvectors for solving data analysis
problems such as clustering. Eigenvectors of large sparse systems must be approximated with iterative methods. This dissertation analyzes how data analysis accuracy depends on the numerical accuracy of the eigensolver. This leads to new bounds on the residual tolerance necessary to guarantee correct partitioning. We present a novel stopping criterion for spectral partitioning guaranteed to satisfy the Cheeger inequality along with an empirical study of the performance on real world networks such as web, social, and e-commerce networks. This work bridges the gap between numerical analysis and computational data analysis.
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Craddock, I. J. "Enhanced numerical techniques for time domain electromagnetic analysis". Thesis, University of Bristol, 1995. http://hdl.handle.net/1983/9ac15a09-f4cd-4971-beb4-80f038c0f561.
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Eid, Rami Samir. "Numerical modelling of geophysical monitoring techniques for CCS". Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/22049.
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I assess the potential of seismic and time-domain controlled-source electromagnetic (CSEM) methods to monitor carbon dioxide (CO2) migration through the application of a monitorability workflow. The monitorability workflow describes a numerical modelling approach to model variations in the synthetic time-lapse response due to CO2 migration. The workflow consists of fluid-flow modelling, rock-physics modelling and synthetic seismic or CSEM forward modelling. I model CO2 injected into a simple, homogeneous reservoir model before applying the workflow to a heterogeneous model of the Bunter Sandstone reservoir, a potential CO2 storage reservoir in the UK sector of the North Sea. The aim of this thesis is to model the ability of seismic and time-domain CSEM methods to detect CO2 plume growth, migration and evolution within a reservoir, as well as the ability to image a migrating front of CO2. The ability to image CO2 plume growth and migration within a reservoir has not been demonstrated in the field of CSEM monitoring. To address this, I conduct a feasibility study, simulating the time-lapse CSEM time-domain response of CO2 injected into a saline reservoir following the multi-transient electromagnetic (MTEM) method. The MTEM method measures the full bandwidth response. First, I model the response to a simple homogeneous 3D CO2 body, gradually increasing the width and depth of the CO2. This is an analogue to vertical and lateral CO2 migration in a reservoir. I then assess the ability of CSEM to detect CO2 plume growth and evolution within the heterogeneous Bunter Sandstone reservoir model. I demonstrate the potential to detect stored and migrating CO2 and present the synthetic results as time-lapse common-offset time sections. The CO2 plume is imaged clearly and in the right coordinates. The ability to image seismically a migrating front of CO2 remains challenging due to uncertainties regarding the pore-scale saturation distribution of fluids within the reservoir and, in turn, the most appropriate rock-physics model to simulate this: uniform or patchy saturation. I account for this by modelling both saturation models, to calculate the possible range of expected seismic velocities prior to generating and interpreting the seismic response. I demonstrate the ability of seismic methods to image CO2 plume growth and evolution in the Bunter Sandstone saline reservoir model and highlight clear differences between the two rock-physics models. I then modify the Bunter Sandstone reservoir to depict a depleted gas field by including 20% residual gas saturation. I assess the importance and implication of patchy saturation and present results which suggest that seismic techniques may be able to detect CO2 injected into depleted hydrocarbon fields.
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Ferguson, R. C. "Numerical techniques for the drift-diffusion semiconductor equations". Thesis, University of Bath, 1996. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362239.
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Jones, R. "Numerical optimisation techniques applied to problems in continuum mechanics". Thesis, University of Nottingham, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378760.
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Tiezzi, Ferdinando. "Planar antennas with inhomogeneities : numerical techniques and software engineering /". [S.l.] : [s.n.], 2003. http://library.epfl.ch/theses/?nr=2706.
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Urlea, Maria. "Numerical Optimization Techniques for Secure Communications Over MIMO Channels". Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31859.
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As multimedia applications become more popular, wireless communication systems are expected to reliably provide increased data rates. Multiple Input Multiple Output (MIMO) technologies can meet this demand without using additional bandwidth or transmit power. MIMO is part of modern wireless communication standards. Another critical aspect of communications is to secure the confidentiality of data transmission. Cryptography accomplishes this at the upper layers of the protocol stack. At the physical layer, data travels unencrypted and can be secured by using the channel characteristics to ``hide'' data transmission from potential eavesdroppers. We consider a Gaussian MIMO wiretap channel and are looking for the maximal rate at which data can be transmitted both reliably and securely to the intended receiver: the secrecy capacity. This quantity is difficult to find analytically and is known precisely in only a few cases. This thesis proposes several numerical optimization methods, both stochastic and deterministic, to evaluate the secrecy capacity and to find the optimal transmit covariance matrix. The stochastic approaches are based on Monte-Carlo and on Differential Evolution (a genetic algorithm). The deterministic approaches are based on successive linear approximation. The accuracy of the results obtained with these methods is, in general, better than the one offered by popular numerical optimization tools such as CVX or YALMIP.
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Nilsson, Martin. "Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain". Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3884.
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Wormald, S. Andrew. "Numerical techniques in digital microscopic holographic particle image velocimetry". Thesis, Loughborough University, 2010. https://dspace.lboro.ac.uk/2134/7140.
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Digital microscopic holographic particle image velocimetry (DµHPIV) is a technique which records scattered coherent light and uses it to measure displacement of particles in a fluid flow. The work in this thesis begins with the construction of a digital holographic microscope and explores the different possible methods of recording and holographic reconstruction, finding an off-axis forward-scatter geometry to be most suitable for the task. A comparison follows of methods to measure displacement in a sparsely seeded environment by performing a simple experiment. It finds that complex amplitude correlation performs significantly better than both intensity correlation and nearest neighbour analysis; the two other possible methods of displacement tracking. Later, an experiment is performed to investigate the behaviour of a microfluidic blood separator. The separator is intended to remove blood plasma from whole blood without other contaminants such as red blood cells and without the need for expensive laboratory equipment. In this chapter a new technique, higher order correlation, is introduced which can be used to strengthen the peaks in correlations of three or more particle images in a flow, and a potential flow CFD model of the separator is built from scratch to predict whether the separator will work, and against which the results can be compared. Finally, there is an experiment carried out which for the first time allows aberration free imaging within objects with irregular, highly curved surfaces; in this case optical fibres and inkjet droplets, by numerically reconstructing the droplet surface.
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Wan, Kin Wa. "Advanced numerical and digital techniques in frequency stability analysis". Thesis, University of Portsmouth, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.237843.
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Aboelnor, Mootaz E. "Advanced numerical techniques to simulate soil-tool interface problems". Thesis, University of Strathclyde, 2002. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=20353.
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In most mine clearing or earth moving equipment such as bulldozers, the working tool is a blade. The blade geometry and operating conditions, such as cutting speed, cutting angle, and cutting depth, have a great effect on overall machine productivity. Most of the published experimental studies confirm these effects. However experimental studies are expensive and their results are highly dependant on the accuracy of measurement devices and the reliability of experimental procedures employed. Numerical techniques have recently shown more promise especially with the current increase in computational power and development of more sophisticated material models. However in order to simulate the soil-tool interface process accurately, careful selection of the appropriate material model for the soil and the interface is required. This should, ideally, be based on a reasonable number of material parameters that have direct physical meaning. In this study a review of the available constitu tive models for soil (particularly sand) and soil-tool interface was carried out. This review study concluded by selecting the so called hypoplastic model as the most appropriate to simulate the sandy soil behavior over a wide range of stresses. Some modifications were carried out on this selected hypoplastic model to optimize it for simulation of the soil-tool interaction process, which is characterized by monotonic loading and high deformation. The modified model was verified numerically and then implemented into the finite element method via an ABAQUS user defined subroutine UMAT. Then the implemented model was verified through analysis of some benchmark problems and results were compared with results from different classical failure criteria. The finite element analysis revealed the high performance of the hypoplastic model in simulating sand behaviour. Finally an analysis of various factors affecting soil-tool interaction was carried out in both two-dimensions and three-dimensions. Results revealed the significant effect of both geometry and operating conditions on blade cutting forces and confirmed the ability of the finite element method to analyze the soil-tool interaction process.
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Marriott, John M. "Bayesian numerical and approximation techniques for ARMA time series". Thesis, University of Nottingham, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329935.
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Sepùlveda, Salas Paulina Ester. "Spacetime Numerical Techniques for the Wave and Schrödinger Equations". PDXScholar, 2018. https://pdxscholar.library.pdx.edu/open_access_etds/4206.
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The most common tool for solving spacetime problems using finite elements is based on semidiscretization: discretizing in space by a finite element method and then advancing in time by a numerical scheme. Contrary to this standard procedure, in this dissertation we consider formulations where time is another coordinate of the domain. Therefore, spacetime problems can be studied as boundary value problems, where initial conditions are considered as part of the spacetime boundary conditions.
When seeking solutions to these problems, it is natural to ask what are the correct spaces of functions to choose, to obtain wellposedness. This motivates the study of an abstract theory for unbounded partial differential operators associated with a general boundary value problem on a bounded domain. A framework for choosing the spaces is introduced, and conditions for the solvability of weak formulations are provided. We apply this framework to study wave problems on tents and to study wellposed discontinuous Petrov-Galerkin (DPG) formulations for the Schrödinger and wave equations. Several numerical issues are also discussed.
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Collinson, Roger. "Mathematical models and numerical techniques for plasticity flows of granular media". Thesis, Curtin University, 1998. http://hdl.handle.net/20.500.11937/1930.
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A mathematical study has been undertaken to model various kinds of granular flows including the perfect plasticity flow and the viscous elasto-plasticity flow. The work is mainly based on the double-shearing theory originated by Spencer and developed by many others. The focus of the project is on the formulation of the theory, the construction of mathematical models and the development of robust simulation techniques.Based on a general formulation of the double-shearing theory, the perfect plasticity flow is shown to be governed by a set of highly nonlinear first order hyperbolic partial differential equations with two distinct characteristics. A sophisticated numerical algorithm is then developed based on the method of characteristics to determine the stress discontinuity and the velocity and stress fields. With the method developed, a numerical study is then undertaken to model the flow of granular materials in a hopper in the presence of stress discontinuity and to investigate the influence of various parameters on the distribution of hopper wall pressures.Utilising the double shearing theory, a set of stress-strain constitutive equations in explicit form has been derived, which makes it possible to formulate the double-shearing theory within the framework of the finite element method. Thus, consequently, a sophisticated finite element technique has been developed to solve the general boundary value problem governing the viscous elasto-plasticity flows obeying the double-shearing theory. Numerical implementation of the frictional boundary condition is also presented. The model is then illustrated with a numerical example demonstrating the influence of wall friction on the distribution of pressures on silo walls throughout the dynamic process of material discharge from silos.
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Reu, Taekyu. "Techniques for compressible flow calculations on multi-zone grids". Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/52327.
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In order to simulate inviscid/viscous compressible flowfields about 3-D realistic aerodynamic bodies, the combined use of an implicit, upwind biased real gas scheme with 3-D fully conservative patched grid techniques is discussed. An "equivalent" gamma formulation is implemented in order to model real gas effects in Van Leer's flux vector splitting (FVS) and Roe’s flux difference splitting (FDS) scheme. A hybrid approximate-factorization (AF)/relaxation algorithm is used as an efficient solver of the Euler, parabolized Navier-Stokes, and thin-layer Navier-Stokes equations. Two different approaches, clipping and Ramshaw’s rezoning algorithms, for performing a conservative flux calculation are described and compared in terms of numerical efficiency. In order to show the real gas \\\ effects in the upwind schemes, two tcst problems are solved. Also to demonstrate the capability of the patched grid approach, the turbulent flowüeld about 3-D analytic forebody is calculated as another test problem. Due to the poor results of the Baldwin-Lomax turbulent model for separated flows, only the attached flowtield is considered in the analytic forebody calculation. Finally, as applications of this approach, the inviscid/viscous flowfields about several aerodynamic bodies are calculated including a generic hypersonic aircraft, a model of the SR-71 aircraft, and F-18 forebody with strakes.Ph. D.
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Dellaportas, Petros. "Imbedded integration rules and their applications in Bayesian analysis". Thesis, University of Plymouth, 1990. http://hdl.handle.net/10026.1/2067.
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This thesis deals with the development and application of numerical integration techniques for use in Bayesian Statistics. In particular, it describes how imbedded sequences of positive interpolatory integration rules (PIIR's) obtained from Gauss-Hermite product rules can extend the applicability and efficiency of currently available numerical methods. The numerical strategy suggested by Naylor and Smith (1982) is reviewed, criticised and applied to some examples with real and artificial data. The performance of this strategy is assessed from the viewpoint of 3 criteria: reliability, efficiency and accuracy. The imbedded sequences of PIIR’s are introduced as an alternative and an extension to the above strategy for two major reasons. Firstly, they provide a rich class of spatially ditributed rules which are particularly useful in high dimensions. Secondly, they provide a way of producing more efficient integration strategies by enabling approximations to be updated sequentially through the addition of new nodes at each step rather than through changing to a completely new set of nodes. Finally, the Improvement in the reliability and efficiency achieved by the adaption of an integration strategy based on PIIR's is demonstrated with various illustrative examples. Moreover, it is directly compared with the Gibbs sampling approach introduced recently by Gelfand and Smith (1988).
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Camphouse, R. Chris. "Modeling and Numerical Approximations of Optical Activity in the Chemical Oxygen-Iodine Laser". Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28640.
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The chemical oxygen-iodine laser (COIL) has several important military and industrial applications. The concern of this work is do develop a partial differential equation model describing optical behavior in the COIL. Optical behavior of the COIL has traditionally been investigated via a ray tracing method. Photons are represented as discrete particles, and their behavior is described by the geometry of the system. We develop an optical model wherein photons have a wave description. In order to construct the mathematical model, we utilize the theory of paraxial wave optics and Gaussian beams. Doing so allows us to incorporate physical effects such as diffusion/diffraction and refraction into the model. After describing the optical model, we present numerical methods for obtaining approximate solutions to the model in the cases of one and two transverse directions. Results are presented illustrating the efficacy of the numerical methods.Ph. D.
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Meister, Neil E. "Application of numerical optimization techniques to surface combatant design synthesis". Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1998. http://handle.dtic.mil/100.2/ADA355524.
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Thesis (M.S. in Mechanical Engineering) Naval Postgraduate School, September 1998."September 1998." Thesis advisor(s): Matthew D. Kelleher, C.N. Calvano. Includes bibliographical references (p. 229-230). Also available online.
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Zhuang, Sicong. "Communication reduction techniques in numerical methods and deep neural networks". Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/668073.
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Inter-node communication has turned out to be one of the determining factors of the performance on modern HPC systems. Furthermore, the situation only gets worse with the ever-incresing size of the cores involved. Hence, this thesis explore the various possible techniques to reduce the communication during the execution of a parallel program. It turned out that there is no one-size-fit-all approach to the challenge. Despite this, the problems in each field, due to their unique characteristics, dispose of distinct opportunities for the communication reduction. The thesis, first devles into numerical linear algebra, develops an evolution of the Pipelined CG called IFCG. It eliminates the synchronizations normally take place towards the end of each iteration to increase the parallelism. Secondly, the thesis draws its attention on reducing the necessity to transfer the parameters between the CPU host and GPUs during a neural network training. It develops two routines: ADT and AWP in order to compress and decompress the weights with a reduced data representation format prior and right after the data transfer takes place. The compress rate is adjusted vis-à-vis the L2-norm of the weights of every layer. In the third contribution, the thesis diminish the communication in model parallelizing a deep neural network. Instead of splitting and distributing the neurons of each layer to the available processes on the system, now it is done every other layers. This results in a 50% percent reduction of the communication whereas it introduces 50% of extra local FP computation.La comunicació entre els nodes de computació multi-core sorgeix com un dels factors principals que impacta el rendiment d’un sistema HPC d’avui en dia. I més, mentre més core es pusa, pitjor la situació. Per tant aquesta tesi explora les possibles tècniques per a reduir la comunicació en l’execució d’un programa paral·lel. Tot i això, resulta que no existeix una sola tècnica que pugui resoldre aquest obstacle. Tot i que els problemes en cada àmbit, com que té els seus propis caracristics, disposa variosos oportunitats per la reducció de comunicació. La tesi, en primer lloc, dins de l’àmbit de l’àlgebra lineal numèriques desenvolupa un algoritme IFCG que és una evolució de Pipelined CG. IFCG elimina les sincronitzacions normalment posa cap al final de cada iteració per augmentar el paral·lelisme. En la segona contribució, la tesi dirigeix l’atenció a reduir la necessitat de transferir els paràmetres entre el CPU i els GPUs durant l’entrenament d’una xarxa neuronal. Desenvolupa rutines ADT i AWP per comprimir i descomprimir els pesos amb una representació de dades reduïda abans i just desprès de la transferència. La representació es decideix dinàmicament segons el L2-norm dels pesos a cada capa. Al final la tesi disminueix la comunicació en paral·lelitzar el model duna xarxa neurona. En lloc de distribuir les neurones de cada capa als processos disponibles en el sistema, es fa cada dues capes. Així que corta com mitja de la comunicació. En canvi, com que distribueix només cada dues capes, les capes restes es repliquen, resulta que incorre en una augmenta de 50% de computació local.
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Saeed, Usman. "Adaptive numerical techniques for the solution of electromagnetic integral equations". Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41173.
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Various error estimation and adaptive refinement techniques for the solution of electromagnetic integral equations were developed. Residual based error estimators and h-refinement implementations were done for the Method of Moments (MoM) solution of electromagnetic integral equations for a number of different problems. Due to high computational cost associated with the MoM, a cheaper solution technique known as the Locally-Corrected Nyström (LCN) method was explored. Several explicit and implicit techniques for error estimation in the LCN solution of electromagnetic integral equations were proposed and implemented for different geometries to successfully identify high-error regions. A simple p-refinement algorithm was developed and implemented for a number of prototype problems using the proposed estimators. Numerical error was found to significantly reduce in the high-error regions after the refinement. A simple computational cost analysis was also presented for the proposed error estimation schemes. Various cost-accuracy trade-offs and problem-specific limitations of different techniques for error estimation were discussed. Finally, a very important problem of slope-mismatch in the global error rates of the solution and the residual was identified. A few methods to compensate for that mismatch using scale factors based on matrix norms were developed.
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Baldwin, Emily Clare. "Investigation of impact crater processes using experimental and numerical techniques". Thesis, University College London (University of London), 2008. http://discovery.ucl.ac.uk/15936/.
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Impact events throughout the history of the Solar System have occurred at all scales, from craters produced by the hypervelocity impact of cosmic dust observed on lunar return samples, to the giant planet-sculpting impacts that have shaped the solid bodies of the Solar System. Investigating the impact process in the laboratory allows us to understand crater formation at a small scale where strength effects dominate; however, it is difficult to scale directly to planetary sized impacts because gravity governs the cratering process at this large scale. Through computer modeling, it is possible to bridge the gap from small to large scale impact events. The influence of target porosity, saturation and an overlying water layer on crater morphology is investigated in the laboratory using a two-stage light gas gun to fire 1 mm diameter stainless steel projectiles at ~5 km s^{-1} into sandstone targets. Larger craters were formed in the higher porosity targets and saturated targets. A critical water depth of 11.6\pm 0.5 times the projectile diameter was required to prevent cratering in an unsaturated target, compared with 12.7\pm 0.6 for saturated targets. The sensitivity of this critical water depth to impact velocity, projectile diameter and density is examined through use of the AUTODYN numerical code, for both laboratory and planetary scale impact events. Projectile survivability into water and sand targets is investigated in the lab for stainless steel and shale projectiles impacting at 2-5 km s^{-1}; up to 30% of the projectile is found to survive. AUTODYN simulations shows that basalt or sandstone meteorites impacting a simulated lunar surface survive the impact at velocities <5 km s^{-1} and at a range of angles, which has positive implications for detecting terrestrial meteorites on the Moon. Groundwork has also been laid for the modelling of the deliberate collision of the SMART-1 spacecraft into the Moon. Finally, lunar and terrestrial impact events are simulated in order to quantify the depth of excavation as a function of transient crater diameter for a range of crater and basin sizes. The output is found to lie in the range 0.08-0.15, with the South Pole Aitken basin excavating material to a depth comparable to the thickness of the farside crust.
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Lu, Zhengxin. "Modelling geotechnical uncertainty using numerical modelling techniques : Kuldip Narbheshankar Modha". Thesis, University of Nottingham, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446386.
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Naderian, Hamidreza. "Advanced Numerical Techniques for Dynamic and Aerodynamic Analysis of Bridges". Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36089.
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To meet the economic, social and infrastructure needs of the community for safe and efficient transportation systems, long span bridges have been built throughout the world. Long span bridges are one of the most challenging kinds of structures in civil engineering. The cable-stayed bridges are of great interest mainly as an alternative and a more economic solution than the one of suspension bridges. In addition, the fiber reinforced polymer (FRP) composites are, nowadays, successfully used for constructing modern bridges, where the significant weight saving provides additional benefits. Because of the great flexibility, modern long-span cable-stayed bridges are usually very susceptible to dynamic loads especially to the earthquake and strong winds. Therefore, the earthquake-resistant and wind-resistant designs become one of key issues for successful construction of bridges.
The objective of the present research is to develop a very efficient spline finite strip technique, for modelling and analysis of both conventional and hybrid FRP cable-stayed bridges. The study falls into the categories of bending, free vibration, seismic, and aerodynamic flutter analysis. The spline finite strip method (SFSM) is one of the most efficient numerical methods for structural analysis of bridges, reducing the time required for estimating the structural response without affecting the degree of accuracy. In the finite strip method, the degrees of freedom could be significantly reduced due to the semi-analytical nature of this method. However, the previous versions of SFSM are not able to model the entire bridge system. For that reason, the structural interactions between different structural components of the bridge could not be handled. In addition, the vibrations and displacements of the towers and cables could not be investigated. In the present formulation, all these obstacles have been eliminated. Moreover, the proposed finite strip technique is very efficient and accurate due to the drastic reduction in the formulation time, simplicity of data preparation, rapid rate convergence of the results, and the semi-analytical nature.
Last but not least, and for the first time, a fully finite strip solution is extended to the area of wind engineering. Using the spline finite strip discretization, the aerodynamic stiffness and mass properties of the long-span cable-stayed bridge are derived. The aerodynamic properties along with the structural properties of long-span plates and bridges are formulated in the aerodynamic equation of motion and are used to analyze the flutter problem.
The accuracy and efficiency of the proposed advanced finite strip method is verified against the finite element and field measurement results. The results demonstrate that this methodology and the associated computer code can accurately predict the dynamic and aerodynamic responses of the conventional and FRP long-span cable-stayed bridge systems. The outcome of the present research will lead to a comprehensive structural analysis of bridges in the framework of the proposed discretization which is more efficient and straightforward than the finite element analysis.
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Collinson, Roger. "Mathematical models and numerical techniques for plasticity flows of granular media". Curtin University of Technology, School of Mathematics and Statistics, 1998. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=10697.
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A mathematical study has been undertaken to model various kinds of granular flows including the perfect plasticity flow and the viscous elasto-plasticity flow. The work is mainly based on the double-shearing theory originated by Spencer and developed by many others. The focus of the project is on the formulation of the theory, the construction of mathematical models and the development of robust simulation techniques.Based on a general formulation of the double-shearing theory, the perfect plasticity flow is shown to be governed by a set of highly nonlinear first order hyperbolic partial differential equations with two distinct characteristics. A sophisticated numerical algorithm is then developed based on the method of characteristics to determine the stress discontinuity and the velocity and stress fields. With the method developed, a numerical study is then undertaken to model the flow of granular materials in a hopper in the presence of stress discontinuity and to investigate the influence of various parameters on the distribution of hopper wall pressures.Utilising the double shearing theory, a set of stress-strain constitutive equations in explicit form has been derived, which makes it possible to formulate the double-shearing theory within the framework of the finite element method. Thus, consequently, a sophisticated finite element technique has been developed to solve the general boundary value problem governing the viscous elasto-plasticity flows obeying the double-shearing theory. Numerical implementation of the frictional boundary condition is also presented. The model is then illustrated with a numerical example demonstrating the influence of wall friction on the distribution of pressures on silo walls throughout the dynamic process of material discharge from silos.
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Okafor, Anthony. "Entropy based techniques with applications in data mining". [Gainesville, Fla.] : University of Florida, 2005. http://purl.fcla.edu/fcla/etd/UFE0013113.
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Siu, Ka Wai. "Numerical algorithms for data analysis with imaging and financial applications". HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/550.
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In this thesis, we study modellings and numerical algorithms to data analysis with applications to image processing and financial forecast. The thesis is composed of two parts, namely the tensor regression and data assimilation methods for image restoration.;We start with investigating the tensor regression problem in Chapter 2. It is a generalization of a classical regression in order to adopt and analyze much more information by using multi-dimensional arrays. Since the regression problem is subject to multiple solutions, we propose a regularized tensor regression model to the problem. By imposing a low-rank property of the solution and considering the structure of the tensor product, we develop an algorithm which is suitable for scalable implementations. The regularization method is used to select useful solutions which depend on applications. The proposed model is solved by the alternating minimization method and we prove the convergence of the objective function values and iterates by the maximization-minimization (MM) technique. We study different factors which affects the performance of the algorithm, including sample sizes, solution ranks and the noise levels. Applications include image compressing and financial forecast.;In Chapter 3, we apply filtering methods in data assimilation to image restoration problems. Traditionally, data assimilation methods optimally combine a predictive state from a dynamical system with real partially observations. The motivation is to improve the model forecast by real observation. We construct an artificial dynamics to the non-blind deblurring problems. By making use of spatial information of a single image, a span of ensemble members is constructed. A two-stage use of ensemble transform Kalman filter (ETKF) is adopted to deblur corrupted images. The theoretical background of ETKF and the use of artificial dynamics by stage augmentation method are provided. Numerical experiments include image and video processing.;Concluding remarks and discussion on future extensions are included in Chapter 4.
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Saha, Reema. "Investigation of a continuum damage model using experimental and numerical techniques". Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/12542.
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Hao, Jinde. "Dynamic responses of soil anchorages using numerical and centrifuge modelling techniques". Thesis, Available from the University of Aberdeen Library and Historic Collections Digital Resources, 2008. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=24846.
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Cadafalch, Rabasa Jordi. "Numerical Simulation of Turbulent Flows. Multiblock Techniques. Verification and Experimental Validation". Doctoral thesis, Universitat Politècnica de Catalunya, 2002. http://hdl.handle.net/10803/6681.
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Work here presented is the result of basic research in key aspects of the currently available engineering tools and methodologies for the design, optimisation and development of thermal systems and equipment: turbulence modelling, high performance computing and quality tests and procedures so as to assess credibility to the numerical solutions (verification and validation). The thesis comprises six main chapters written in a paper format. Two of them have already been published in international journals, one in the proceedings of a Spanish conference and two in proceedings of international conferences on Computational Fluid Dynamics and heat transfer. The last chapter has recently been submitted for publication to an international journal. Therefore, all the chapters are written so as to be self-contained, complete and concise. As a consequence, some contents of the chapters such those describing the governing equations, or the verification procedure used to assess the credibility of the numerical solutions, are repeated in several of them. Furthermore, as only minor changes have been introduced in the chapters respect to the original papers, each of them reflects the know-how of the CTTC (Heat and Mass Transfer Technological Centre were the research has been carried out) when they were published.
Papers presented in chapters 1 and 2 deal with turbulence modelling. A general overview is given on the formulation and numerical techniques of the different levels of turbulence modelling: Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and Reynolds Averaged Navier-Stokes Simulation (RANS). Main attention is focussed on the eddy viscosity two-equation RANS models. Their formulation is presented in more detail, and numerical solutions of the most extended. Benchmark problems on turbulence modelling are given compared to the available experimental data.
Chapters 3 and 4 focus on the use of the multiblock method (domain decomposition method), as a numerical technique that combined with the parallel computing may allow reducing the demanding computational time and memory (high performance computing). The multiblock approach used is based on the conservation of all the physical quantities (fully conservative method) and on an explicit information exchange between the different blocks of the domain. The goal of the work presented in these two chapters is to verify that such a multiblock approach does not introduce additional uncertainty in the numerical solutions.
Chapter 5 presents a tool that has been developed at the CTTC for the verification of finite volume computations. In fact, this tool is also partially used and described in the results presented in the previous chapters. Here, it is described and discussed in detail and it is applied to a set of different CFD and heat transfer problems in two and three dimensions, with free and forced convection, with reactive and non-reactive flows and with laminar and turbulent flows.
The last chapter shows a complete study for the development of a credible heat transfer relation for the heat evacuated from a ventilation channel. Such study comprises all the different steps that have to be accomplished so as to develop credible and applicable results in mechanical engineering. It comprises a description of the mathematical model to represent the physical phenomena in the channel, the numerical model to solve the set of coupled differential equations of the mathematical model, the construction and testing of an ad-hoc experimental set-up, and a verification and validation (V&V) test that guarantees that the numerical solution is an accurate enough approximation of the mathematical model (verification), and that it properly predicts the reality (validation).
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He, Xin. "On some Numerical Methods and Solution Techniques for Incompressible Flow Problems". Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-179410.
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The focus of this work is on numerical solution methods for solving the incompressible Navier-Stokes equations, which consist of a set of coupled nonlinear partial differential equations. In general, after linearization and finite element discretization in space, the original nonlinear problem is converted into finding the solutions of a sequence of linear systems of equations. Because of the underlying mathematical model, the coefficient matrix of the linear system is indefinite and nonsymmetric of two-by-two block structure. Due to their less demands for computer resources than direct methods, iterative solution methods are chosen to solve these linear systems. In order to accelerate the convergence rate of the iterative methods, efficient preconditioning techniques become essential. How to construct numerically efficient preconditioners for two-by-two block systems arising in the incompressible Navier-Stokes equations has been studied intensively during the past decades, and is also a main concern in this thesis. The Navier-Stokes equations depend on various problem parameters, such as density and viscosity, that themselves may vary in time and space as in multiphase systems. In this thesis we follow the following strategy. First, we consider the stationary Navier-Stokes equations with constant viscosity and density, and contribute to the search of efficient preconditioners by analyzing and testing the element-by-element approximation method of the Schur complement matrix and the so-called augmented Lagrangian method. Second, the variation of the viscosity is an important factor and affects the behavior of the already known preconditioners, proposed for two-by-two block matrices. To this end, we choose the augmented Lagrangian method and analyse the impact of the variation of the viscosity on the resulting preconditioner. Finally, we consider the Navier-Stokes equations with their full complexity, namely, time dependence, variable density and variable viscosity. Fast and reliable solution methods are constructed based on a reformulation of the original equations and some operator splitting techniques. Preconditioners for the so-arising linear systemsare also analyzed and tested.
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Xu, Yizhong. "Wind shielding analysis for cold regions using experimental and numerical techniques". Thesis, University of Hertfordshire, 2016. http://hdl.handle.net/2299/17237.
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The thesis presents a systematic experimental and numerical study on the interactions among porous fence, airflow, and windblown snowdrifts, a knowledge that will contribute to optimize the performance of porous wind shielding system in Cold Regions. A comprehensive review of the concepts, theories, techniques, and key findings associated with the research work has been undertaken. The key technical parameters influencing fence performance have been systematically studied by means of wind tunnel experimental investigations and Computational Fluid Dynamics (CFD) simulations. The study has found that porosity is the most influential structural parameter affecting the performance of porous fences in many aspects. Fence height stands a significant positive position in terms of its performance. It was found that fence performance is not sensitive to the changes of approaching atmospheric airflow velocity. Nevertheless, a bottom gap can improve snow fence trap efficiency. All of those findings agree with most of the findings of other researchers, which affirms that the research methodology adopted in this research is sound. Physical experimental work was performed to assess the reliability and credibility of the numerical models. Those models have been intentionally simplified, which made them easier to construct and quicker to obtain numerical solutions at a lower computational cost. Furthermore, the numerical models demonstrate the level of competence acquired through this research that is implemented in the optimisation of fence design. Special attention has been paid to the issues where elaborate research work has not been systematically reached in the open literature, this includes areas such as the effects of arrangement of porous holes, fence surface shear, and directions of wind load with respect to the fence, etc. Correlation between the reattachment length, the shelter distance, and the creation and distribution of fence surface shear is reported, to the author's knowledge, for the first time in the open literature. General guidelines for the design of shelters based on porous fences have been established through this study. For example, the desirable size of hole range should be identified beforehand, and porous holes with sharp angular corners should usually be avoided in the fence design. It is recommended to place the fence within an angle of 30° to the wind load, where the effective shelter distance can be estimated in a linearized equation, and the normal drag coefficient can be described as a function of cos2θ. Optimal design of the arrangement of porous holes will maximize the fence performance, especially when the close fence environment is of concern. Although the definition of fence effective zone is still vague in the research field, the key factors influencing the fence effective zone have been investigated by evaluating the reduction of wind velocity leeward of the fence in this thesis. It is found that the fence effective zone is not sensitive to the change of approaching airflow velocity, and that increasing fence height will increase the physical size of the fence effective zone, but not in a proportional manner. It is also concluded that fence effective zone will be significantly reduced when the non-normal wind load is inclined at an angle greater than 30° to the fence. The effective zone increases effectively when the fence porosity is optimal. In contrast to the majority of published research work, the transient snow transport model presented in this work considers the snow transport rate as a whole without distinguishing the rate in saltation and suspension layer. The numerical study indicated that the position of the snow crest is mainly determined by the fence height, while porosity and bottom gap mainly affect the downwind deposition length. The optimal porosity for snow fences is in the range of 0.4 to 0.5, which is greater than the one for wind fences, which lies in the range from 0.25 to 0.35. Two snow crests have been observed leeward the fence at the onset of snow deposition, when the fence was placed without a bottom gap to the snow ground. This finding has not been encountered in any of the reported research work. Wind tunnel simulations of snowdrift around the fences have marginally under-predicted the sizes of snow deposition. The numerical predictions were quantitatively and qualitatively in good agreement with the field observations. This incompetence of wind tunnel experiments on porous fences implies that numerical modelling can play a more important role in snow fence research.
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Choptuik, Matthew William. "A study of numerical techniques for radiative problems in general relativity". Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/27043.
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There is continuing interest in the numerical solution of the field equations of general relativity. Many of the most interesting scenarios involve the generation and propagation of gravitational radiation—this thesis is an investigation of numerical techniques which should be useful for such problems. The study is based on a model system of a single massless scalar field coupled to the gravitational field, with the additional requirement of spherical symmetry. The 3+1 formalism for numerical relativity is used and attention is limited to finite difference techniques.
As a preliminary step, the properties of some difference schemes are examined in the context of the wave equation in general coordinates. The accuracy, stability, convergence, dissipation, dispersion and efficiency of the schemes are discussed and three of the methods, which are all centred, second order approximations, are identified as being suitable for radiation problems in general relativity.
Following work by Piran, the model problem is solved in three different coordinate systems using variations of the schemes devised for the wave equation. Various initial configurations of the scalar field are evolved, ranging from cases where there is a negligible amount of gravitational self-interaction to those where black holes are formed. Although some numerical difficulties remain with the latter calculations, the basic difference techniques developed for the treatment of the radiative degrees of freedom are found to be satisfactory.
In the past it has been argued that there is a fundamental inconsistency in finite difference solutions of Einstein's equations which are generated by algorithms that do not continuously impose the constraint equations which arise from the coordinate freedom of general relativity. The deviations of freely evolved quantities from discrete versions of the constraint equations are supposedly of lower order (in the mesh spacing) than the underlying difference scheme. An argument based on Richardson's hypothesis concerning the expansion of the error of a difference solution in powers of the mesh spacing is made which suggests that there should be no such inconsistency. Numerical results from two fully second order algorithms are presented in support of this argument.
The remainder of the thesis deals with the application of local mesh refinement techniques to the model problem. A simplified version of a recent algorithm due to Berger and Oliger is implemented for one particular coordinate system and is used to examine the nature of the scalar field's gravitational self-interaction.Science, Faculty of
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Ariyadasa, A. "Filtering and extrapolation techniques in numerical solution of ordinary differential equations". Thesis, University of Ottawa (Canada), 1985. http://hdl.handle.net/10393/4595.
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Noreland, Daniel. "Numerical Techniques for Acoustic Modelling and Design of Brass Wind Instruments". Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3507.
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McCollum, Clarence B. "Numerical analysis of the magnetic slider/disk interface using optimization techniques". Thesis, Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/16083.
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Groves, T. C. (Thomas Cameron). "The cross : a long poem using the techniques of numerical composition". Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=26272.
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The Cross is a long poem with a numerologically determined structure. In my introduction I examine some of the ideas behind the tradition of literary numerological composition, particularly those presented in the Timaeus of Plato and in Augustine's De musica. I then scrutinize number's aptness as a unifying principle in the poem, briefly elucidating the Golden Proportion and showing its centrality to the poem's structure, concluding with a look at my use of number metaphor. The Cross, partly and wholly the embodiment of these theories, follows. Its subject matter is the history of Montreal. Each book has a unifying focus: Book I centres on Jacques Cartier's explorations in 1535; Book II on the activities of the fictional character Mrs. Chau, in the recent past; and Book III on the visit of the Prince of Wales in 1860 for the inauguration of the Victoria Bridge.
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Al-Wahab, Muhanad M. S. "Investigation on the use of different numerical techniques in CAD systems". Thesis, Brunel University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.292384.
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