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Vinikoff, Nicolas. "Numerical Control: Performance Analysis and Implementation Issues". Thesis, KTH, Reglerteknik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-101797.
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In this thesis, a digitalization method with nite word-length (resolu- tion N ) of a given stable analog controller guaranteeing the minimum dierence in terms of frequency responses is treated. The challenge has consisted in nding a relevant frequency responses mismatch met- ric and in relating it to the word niteness issue. The analog con- troller is represented in modal state-space form and digitalized with a stability-maintaining approximation (ramp invariance) for dierent sampling periods. It results in digital controllers with block diago- nal transition matrices whose coecients (poles) are inside the unit circle. The format is chosen to match the poles dynamical range. The matrix is then coded and the mismatch measure allows for the selection of the "best" poles coded controllers. The remaining ma- trices are then scaled and coded for these selected controllers. The measure is computed for each of them. The procedure nally gives the "optimal" coded controller. This algorithm is shown to perform well and better that a simple rounding after the analog controller discretization phase. iii
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Schwarz, Cornelia. "Numerical implementation of continuum dislocation-based plasticity". kostenfrei, 2007. http://mediatum2.ub.tum.de/doc/618976/document.pdf.
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CASTAGNOLI, JOAO PAULO. "NUMERICAL IMPLEMENTATION OF ACOPPLING SURFACE WATER: GROUNDWATER". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=11037@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
A relação entre os processos hidrológicos de escoamento superficial e subterrâneo apresenta uma grande variabilidade espacial e temporal. Podendo ser representado de forma qualitativa como parte sequêncial do ciclo hidrológico, estes processos, demostram sua grande dependência e importância nos estudos de balanços hídricos. Visando uma representação quantitativa, este trabalho faz o acoplamento, entre os modelos numéricos de escoamento superficial e de fluxo em meios porosos. Para o meio poroso adotou-se o modelo numérico SWMS_3D (Simunek et al, 1995), o qual resolve a equação de Richards, para fluxo em meios porosos saturados e não saturados nas três dimensões. Na simulação da dinâmica superficial, foram desenvolvidos dois modelos derivados das equações de Saint- Venant: o modelo da Onda Cinemática e o modelo de Difusão. Para a solução numérica foi empregado o método dos elementos finitos através da formulaçao de Galerkin, adotando uma malha tridimensional de elementos tetraédricos, formando uma sub-malha de elementos triangulares na superfície. O modelo de escoamento superficial emprega a malha triangular e interage com o programa SWMS_3D modificado (que utiliza a malha de tetraédros) através das imposições das condições de contorno transientes. Este, responderá com uma parcela de fluxo correspondente à recarga ou descarga no contorno a cada passo de tempo. Com isso, o modelo gerado é capaz de quantificar espacialmente e temporalmente as cargas de pressão em todos os pontos do domínio de estudo.
While analyzing the interaction between the hydrological processes of surface and groundwater flow, it is seen that there is a big difference in its interaction in the space and time. These processes can be represented in a qualitative form as part of the hydrological cycle, demonstrating its dependences and importance in the hydrological balance. This work does the numerical coupling of the surface and groundwater flow. This work adopted the SWMS_3D numerical model (Simunek et. al., 1995), which resolves the Richards equation for saturated and non saturated porous media flow in 3D. In order to simulate the superficial dynamic flow, two models from Saint-Vennat equation were developed, these models are: the cinematic wave model and the diffusion model. These two models consider the average outflow in sections in a 2D scenario. For the numerical solution the finite element method was adopted through the Galerkin formulation. Adopting a 3D domain mesh of tetrahedral elements, seen from above, in 2D, we can see a triangular element mesh. The superficial flow model uses the triangular mesh and iterates with the SWMS_3D modified software, which uses the tetrahedral elements mesh. This was done by changes in the boundary conditions to the models. The SWMS_3D will answer with a flow portion corresponding to a sink or source action in the surface, in each time step. Finally the generated model is able to quantify in space and in time the pressure head in the study domain.
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Herdiana, Ratna. "Numerical methods for SDEs - with variable stepsize implementation /". [St. Lucia, Qld.], 2003. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17638.pdf.
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Fooladi, Samaneh y Samaneh Fooladi. "Numerical Implementation of Elastodynamic Green's Function for Anisotropic Media". Thesis, The University of Arizona, 2016. http://hdl.handle.net/10150/623144.
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Displacement Green's function is the building block for some semi-analytical methods like Boundary Element Method (BEM), Distributed Point Source Method (DPCM), etc. In this thesis, the displacement Green`s function in anisotropic media due to a time harmonic point force is studied. Unlike the isotropic media, the Green's function in anisotropic media does not have a closed form solution. The dynamic Green's function for an anisotropic medium can be written as a summation of singular and non-singular or regular parts. The singular part, being similar to the result of static Green's function, is in the form of an integral over an oblique circular path in 3D. This integral can be evaluated either by a numerical integration technique or can be converted to a summation of algebraic terms via the calculus of residue. The other part, which is the regular part, is in the form of an integral over the surface of a unit sphere. This integral needs to be evaluated numerically and its evaluation is considerably more time consuming than the singular part. Obtaining dynamic Green's function and its spatial derivatives involves calculation of these two types of integrals. The spatial derivatives of Green's function are important in calculating quantities like stress and stain tensors. The contribution of this thesis can be divided into two parts. In the first part, different integration techniques including Gauss Quadrature, Simpson's, Chebyshev, and Lebedev integration techniques are tried out and compared for evaluation of dynamic Green’s function. In addition the solution from the residue theorem is included for the singular part. The accuracy and performance of numerical implementation is studied in detail via different numerical examples. Convergence plots are used to analyze the numerical error for both Green's function and its derivatives. The second part of contribution of this thesis relates to the mathematical derivations. As mentioned above, the regular part of dynamic Green's function, being an integral over the surface of a unit sphere, is responsible for the majority of computational time. From symmetry properties, this integration domain can be reduced to a hemisphere, but no more simplification seems to be possible for a general anisotropic medium. In this thesis, the integration domain for regular part is further reduced to a quarter of a sphere for the particular case of transversely isotropic material. This reduction proposed for the first time in this thesis nearly halves the number of integration points for the evaluation of regular part of dynamic Green's function. It significantly reduces the computational time.
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Sotolongo, Wilfredo. "On the numerical implementation of cyclic elasto-plastic material models". Thesis, Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/17594.
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QUISPE, ROBERTO JUAN QUEVEDO. "NUMERICAL IMPLEMENTATION FOR 3D ANALYSIS OF TRANSIENT FLOW IN DAMS". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=12189@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOEsta dissertação tem por objetivo a implementação de uma ferramenta numérica para avaliação do fluxo transiente 3D saturado-não saturado em barragens de terra e enrocamento, baseado no método dos elementos finitos e no programa GEOFLUX implementado por Machado Jr. (2000) para análise de problemas 2D. Nesta nova versão, foram incluídos elementos triangulares de 3 nós para análises 2D e elementos tetraédricos de 4 nós para análises 3D. Implementam-se também subrotinas que oferecem a possibilidade de variação das condições de contorno com o tempo. A equação de Richards é solucionada considerando a formulação mista e o método iterativo de Picard Modificado para solução do sistema de equações não- lineares. Para a solução do sistema de equações utiliza-se um armazenamento especial para matrizes esparsas associado com o método do gradiente bi-conjugado, tornando o processo muito rápido, mesmo em sistemas de grande porte. Utilizam- se dois modelos para representar as curvas características: o modelo exponencial proposto por Srivastava e Yeh (1991) e o modelo proposto por van Genuchten (1980). O programa computacional desenvolvido (GEOFLUX3D) foi aplicado na análise de fluxo na barragem de enrocamento de Gouhou, China, e na barragem de terra Macusani, Peru. Os resultados numéricos indicam a necessidade de análises numéricas 3D em barragens situadas em vales estreitos, onde os efeitos de geometria nas condições de fluxo são significativos e não podem ser ignorados.
The main objective of this thesis is to implement a numerical tool for the evaluation of 3D saturated / unsaturated transient flow through earth and rockfill dams with basis on the finite element method and a computer program written by Machado Jr. (2000) for analysis of similar 2D flow problems. In the 3D version, developed in this thesis, four-nodes tetrahedral elements were implement as well as special subroutines that make possible to vary in time the boundary conditions. The Richards` equation is solved through a mixed formulation, for the solution of the non-linear system of equations a Modified Picard`s method is employed. A special algorithm is used to store the sparse matrices which, in association with the bi-conjugated gradient method, rend the solver computationally very efficient, even for a large number of equations. Two different models were used to represent the characteristic curves: the exponential curve proposed by Srivastava and Yeh (1991) and the formulation suggested by van Genuchten (1980). The improved computer program, thereafter named GEOFLUX3D, was then applied for flow analysis of the Gouhou rockfill dam (China) and the Macusani earth dam (Peru). Numerical results point out that 3D numerical analyses are necessary for dams situated in narrow valleys, where the influence of the terrain geometry on the flow conditions are quite significant and cannot be just ignored.
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Mashalaba, Qaphela. "Implementation of numerical Fourier method for second order Taylor schemes". Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/30978.
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The problem of pricing contingent claims in a complete market has received a significant amount of attention in literature since the seminal work of Black, Fischer and Scholes, Myron (1973). It was also in 1973 that the theory of backward stochastic differential equations (BSDEs) was developed by Bismut, Jean-Michel (1973), but it was much later in the literature that BSDEs developed links to contingent claim pricing. This dissertation is a thorough exposition of the survey paper Ruijter, Marjon J and Oosterlee, Cornelis W (2016) in which a highly accurate and efficient Fourier pricing technique compatible with BSDEs is developed and implemented. We prove our understanding of this technique by reproducing some of the numerical experiments and results in Ruijter, Marjon J and Oosterlee, Cornelis W (2016), and outlining some key implementationl considerations.
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Chun, Byung Kwan. "Study on hardening models and numerical implementation for springback prediction /". The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486397841222103.
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He, Ting. "[pi]Mesh : practical implementation of a low-cost wireless mesh for indoor networking /". View abstract or full-text, 2010. http://library.ust.hk/cgi/db/thesis.pl?CSED%202010%20HE.
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Keeve, Michael Octavis. "Study and implementation of Gauss Runge-Kutta schemes and application to Riccati equations". Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/30956.
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Hamed, Maien Mohamed Osman. "On meshless methods : a novel interpolatory method and a GPU-accelerated implementation". Thesis, Nelson Mandela Metropolitan University, 2013. http://hdl.handle.net/10948/d1018227.
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Meshless methods have been developed to avoid the numerical burden imposed by meshing in the Finite Element Method. Such methods are especially attrac- tive in problems that require repeated updates to the mesh, such as problems with discontinuities or large geometrical deformations. Although meshing is not required for solving problems with meshless methods, the use of meshless methods gives rise to different challenges. One of the main challenges associated with meshless methods is imposition of essential boundary conditions. If exact interpolants are used as shape functions in a meshless method, imposing essen- tial boundary conditions can be done in the same way as the Finite Element Method. Another attractive feature of meshless methods is that their use involves compu- tations that are largely independent from one another. This makes them suitable for implementation to run on highly parallel computing systems. Highly par- allel computing has become widely available with the introduction of software development tools that enable developing general-purpose programs that run on Graphics Processing Units. In the current work, the Moving Regularized Interpolation method has been de- veloped, which is a novel method of constructing meshless shape functions that achieve exact interpolation. The method is demonstrated in data interpolation and in partial differential equations. In addition, an implementation of the Element-Free Galerkin method has been written to run on a Graphics Processing Unit. The implementation is described and its performance is compared to that of a similar implementation that does not make use of the Graphics Processing Unit.
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Danas, Konstantinos. "Heterogeneous materials with evolving microstructure : constitutive modeling, numerical implementation and applications". Phd thesis, Ecole Polytechnique X, 2008. http://pastel.archives-ouvertes.fr/pastel-00004107.
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Le travail de thµese porte sur l'application de la methode non-lineaire d' homogeneisation dite du second- ordre de Ponte Casta~neda (2002) pour estimer le comportement effectif des materiaux poreux viscoplastique. A titre de rappel, cette methode est basee sur la construction des principes variationnels appropries en utilisant un composite lineaire de comparaison pour produire des evaluations correspondantes µa des milieux poreux non-lineaires. Ainsi, l'objectif principal de ce travail est de proposer un modµele constitutif general qui tient compte de l' evolution de la microstructure, et par consequent, de l'anisotropie induite par l'application de deformations nies au materiau poreux. Le modele est construit pour reproduire exactement le comportement d'un assemblage de sphere composites dans la limite des chargements hydrostatiques, et concide donc avec la limite hydrostatique du critere de Gurson (1977) pour des materiaux poreux plastiques avec des microstructures isotropes. En consequence, ce nouveau modµele ameliore les estimations d'homogeneisation existantes, lesquelles sont satisfaisantes pour de faibles triaxialites mais excessivement raides pour des triaxialites et des non-linearites elevees. En outre, les estimations obtenues par le modµele dependent de la troisieme invariable du tenseur macroscopique des contraintes, lequel porte un effet non negligeable sur la reponse eective du materiau pour de moyennes et hautes triaxialites. De plus, les resultats cites ci-dessus ont ete generalises µa des microstructures anisotropes complexes (par exemple : des microstructures avec des formes et des orientations arbitraires des pores) et a des chargements tridimensionnels, conduisant a la reponse anisotrope globale du materiau poreux. Le modele est ensuite etendu pour tenir compte de l'evolution de la microstructure lorsque le materiau est soumis µa des deformations nies. Enn, la validation du modµele propose a ete realisee par le biais de calculs par elements ¯nis sur des mi-crostructures axisymetriques periodiques, et donnent des resultats pertinents pour l'ensemble des triaxialites et des non-linearites envisagees.
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Knezevic, David J. "Analysis and implementation of numerical methods for simulating dilute polymeric fluids". Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:b54ad447-86ff-40af-a83e-022f2f0cbabb.
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In this thesis we develop, analyse and implement a number of numerical methods for simulating dilute polymeric fluids. We use a well-known model in which the polymeric fluid is represented by a suspension of dumbbells in a Newtonian solvent. This model is governed by a coupled Navier–Stokes–Fokker–Planck system of partial differential equations, in which the Fokker–Planck equation is posed on a high-dimensional domain. We first thoroughly analyse a Galerkin spectral method for the Fokker–Planck equation in configuration space, before combining this method with a finite element scheme in physical space to obtain an alternating-direction method for the high-dimensional Fokker–Planck equation. Alternating-direction methods have been considered previously in the literature for this problem, but this approach has not been subject to rigorous numerical analysis before. We develop many theoretical results for our numerical algorithms, and we focus particularly on establishing stability and convergence estimates. The numerical methods we develop are fully-practical, and we present a range of numerical results demonstrating their accuracy and efficiency. We also introduce a coupled numerical algorithm for the Navier–Stokes–Fokker–Planck system, which we use to simulate polymeric fluid flow problems of physical interest. The numerical method for the high-dimensional Fokker–Planck equation is the most computationally intensive part of this coupled algorithm, but it is well suited to implementation on a parallel computer, and we exploit this fact to make large-scale computations feasible.
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Eremin, Aleksandr. "Numerical implementation of the wave-turbulence closure in a rotating channel". Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEC031.
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L’étude porte sur un problème de turbulence dans un canal mis en rotation rapide. Dans ce cas, la non linéarité est dominée par la rotation, ce qui suggère d’utiliser la théorie de la turbulence d’ondes.La première partie de ce travail porte sur l’étude du modèle de fermeture pour la turbulence d’ondes (WTC pour « wave-turbulence closure »). Nous exprimons le champ de vitesse comme combinaison de modes de guide d’onde inertiels. Le confinement en canal implique aussi une discrétisation de la composante du vecteur d’onde normale à la paroi. Le transfert non linéaire est dominé par les interactions résonantes entre triades de vecteurs d’ondes. La viscosité, qui se manifeste par l’amortissement des modes, est la somme de deux contributions : l’une volumique, l’autre due à la paroi. Le taux d’amortissement en volume croît comme le carré du nombre d’onde, et inhibe la cascade d’énergie en-deçà d’une certaine échelle de longueur.L’implémentation numérique du modèle utilise un schéma d’avancement en temps qui assure la propriété de réalisabilité du modèle ainsi que la prise en compte des discontinuités spectrales prédites par la théorie de turbulence d’ondes. Les résultats de notre étude numérique du modèle WTC montrent que l’évolution en temps de la turbulence se produit en deux phases. Pendant la première phase, l’amortissement dû à la paroi est dominant, mais à la suite de la cascade d’énergie vers les petites échelles, l’amortissement volumique prend le dessus pendant la seconde phase. Lorsque le coefficient d’amortissement volumique est suffisamment petit, la transition entre les deux phases se produit brusquement à un instant qui est indépendant à la fois des coefficients d’amortissement volumique et de paroi, mais qui varie significativement avec le troisième paramètre du problème qu’est la largeur spectrale initiale. L’évolution du spectre révèle le développement d’une zone inertielle dont la pente se trouve presque indépendante des paramètres du problème. Le transfert d’énergie parallèlement aux parois du canal apparaît être plus efficace que dans la direction normale.En vue de réaliser des simulations numériques directes (DNS pour « Direct Numerical Simulations »), il a fallu développer une méthode appropriée à l’initialisation d’un champ de vitesse possédant les propriétés statistiques prescrites par le modèle. La comparaison des résultats de DNS et de WTC nécessite la construction de la matrice spectrale aux temps ultérieurs. Ceci a nécessité le développement de méthodes d’analyse spectrale et leur incorporation au sein du code de DNS existant. Malgré l’utilisation d’un super-calculateur et du calcul massivement parallèle, seuls trois calculs de DNS ont été possibles. Ces calculs utilisent les mêmes paramètres physiques mais différentes périodes spatiales pour la DNS, afin de vérifier la convergence en fonction des paramètres numériques. Idéalement, de nombreuses réalisations devraient être lancées et une moyenne d’ensemble prise pour calculer la matrice spectrale. Ceci n’étant pas possible avec un seul calcul, nous avons plutôt développé une méthode s’appuyant sur l’isotropie statistique dans les directions parallèles aux parois, dans laquelle les moyennes sont faites sur des domaines annulaires de l’espace spectral. Malheureusement, nos résultats indiquent que la non linéarité n’est pas suffisamment faible au nombre de Rossby utilisé dans les DNS. Par conséquent, un abaissement supplémentaire du nombre de Rossby serait nécessaire pour atteindre le régime d’applicabilité de la théorie de turbulence d’ondes. Ceci n’est cependant pas envisageable avec la puissance de calcul à dispositionA problem of turbulence in a rapidly rotating channel is investigated. The rapid rotation means that nonlinearity is dominated by rotation suggesting application of wave-turbulence theory.The first part of the work is devoted to study of the wave-turbulence closure (WTC) model. We express the velocity field as a combination of inertial waveguide modes. In its turn, confinement implies discretization of the wall-normal component of the wave vector. The nonlinear transfer is dominated by resonant interactions of wave-vector triads. Viscosity is present via modal damping, which is the sum of two components: volumetric and wall damping. The volumetric-damping rate grows as the square of the wavenumber inhibiting the energy cascade below a certain scale.The numerical implementation of the model uses a time-marching scheme ensuring the realizability property of the model and explicit consideration of the spectral discontinuities predicted by the wave-turbulence theory. According to the results of numerical investigation of the WTC model the time evolution of the turbulence occurs in two phases. During the first phase wall damping dominates, but following an energy cascade to the small scales, volumetric damping takes over during the second phase. Provided the volumetric-damping coefficient is sufficiently small, the transition between the phases takes place abruptly at a time which is insensitive to both wall- and volumetric- damping coefficients, but varies significantly with the third parameter of the problem, which is the initial spectral width. Evolution of the spectra reveals the development of an inertial range whose exponent is found to be almost independent of the problem parameters. The transfer of energy parallel to the channel walls is found to be more efficient than in the cross-channel direction.To perform direct numerical simulations (DNS) an appropriate method for initialization of the velocity field possessing the statistical properties prescribed by the model is developed. Comparison of the DNS and WTC results requires construction of the spectral matrix at later times. This involved the development of spectral analysis methods and their incorporation into the existing DNS code. Despite running the DNS on a super-computer and using many processors in parallel, only three runs were feasible. Those runs used the same physical parameters and different DNS spatial periods to check for convergence with respect to that numerical parameter. In an ideal world, many realizations would be performed and the ensemble average taken to calculate the spectral matrix. Given one run, this is not possible, so we instead developed a method based on statistical isotropy in the directions parallel to the walls in which averages are taken over annular regions in spectral space. Unfortunately, the results indicate that nonlinearity is not small enough for the Rossby number used in the DNS. That is, further reduction of the Rossby number would be needed to reach the regime of applicability of the wave-turbulence theory. This is not achievable with the computer power available
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Rana, Muhammad Sohel. "Analysis and Implementation of Numerical Methods for Solving Ordinary Differential Equations". TopSCHOLAR®, 2017. https://digitalcommons.wku.edu/theses/2053.
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Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number of practical fields such as equations arising in population dynamics and astrophysics. It includes discussion what are the advantages and disadvantages of implicit methods over explicit methods, the accuracy and stability of methods and how the order of various methods can be approximated numerically. Also, semidiscretization of some partial differential equations and stiff systems which may arise from these semidiscretizations are examined.
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CIOCIOLA, GIUSEPPE. "Dynamics of Commodity Prices. A Potential Function Approach with Numerical Implementation". Doctoral thesis, Università degli studi di Bergamo, 2013. http://hdl.handle.net/10446/28630.
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In the present analysis a nonlinear model is discussed in order to capture the presence of several forces acting in commodity markets and the difficulty to disentangle their relative price impacts. Global commodity markets have experienced significant price swings in recent years. Analysts offer two explanations: market forces and speculative expectations, not mutually exclusive. Commodity prices seem to indicate that various factors are acting in a very complex way. We start from one specific feature: price clustering phenomenon, which is the tendency to concentrate in a number of attraction regions, preferring some values over others. Commodities are in the process of becoming mainstream. The mean-reverting class of diffusion models are not able to model the phenomenon of multiple attraction regions. In the potential function approach the price is modelled as a diffusion process governed by a potential function. A fundamental step is to fit the multimodal density of the invariant distribution. We postulate a parametric form of the distribution in the framework of finite mixture models and Expectation-Maximization algorithm. The procedure for identifying and estimating potential function and diffusion parameter is provided. Applications to crude oil and soybean prices capture the essential characteristics of the data remarkably well. An underlying assumption is that potential function and long-term volatility do not change with time. New market conditions and new attraction regions can form, changing the shape of the potential and the magnitude of long-term volatility. We investigate changes in shape of the potential, which reflects new price equilibrium levels (attraction regions) and hence new market conditions. The model allows to generate copies of the observed price series with the same invariant distribution, useful for applications requiring a large number of independent price trajectories. A goodness-of-fit test for the SDE model is provided. A numerical implementation of the analysis is provided.
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Huang, Chien-Wei. "Development and numerical implementation of nonlinear viscoelastic-viscoplastic model for asphalt materials". [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-3137.
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Powers, Lynn M. "Mechanical behavior of ceramics at high temperatures constitutive modeling and numerical implementation /". online version, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=case1149816510.
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ANDRADE, HEBER AUGUSTO COTARELLI DE. "IMPLEMENTATION OF NUMERICAL PROCEDURES FOR THE ANALYSIS OF DRAINING ELEMENTS IN SOILS". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=4301@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOEsta pesquisa visa o desenvolvimento de uma ferramenta numérica capaz de simular a inclusão de elementos drenantes em solos, sejam eles representados por drenos subhorizontais ou poços, constituindo sistemas de drenagem amplamente utilizado em estabilidade de encostas, túneis, escavações e outros. A implementação foi gerada nos programas de fluxo SWMS_2D e SWMS_3D (Simunek e outros, 1994). A formulação proposta considera a equação de fluxo do elemento drenante e a estratégia numérica de sua inclusão na equação de fluxo do solo pelo método dos elementos finitos. Algumas análises numéricas foram realizadas visando a validação do algoritmo. Para os poços foram analisados os casos confinados e não confinados e em regime permanente e transiente, comparando as soluções numéricas obtidas com as soluções analíticas de Theis (1935) (Freeze, 1979), para aqüífero confinado, e de Neumann (1975), para aqüífero não confinado. Para os drenos subhorizontais, propõe - se aqui uma metodologia de análise, levando em consideração os parâmetros hidráulicos e geométricos de um elemento de dreno. Sua aplicação atual não requer muito rigor e este estudo vem com a proposta de ser uma ferramenta geotécnica na fase de projeto de uma obra.
This research aims at the development of a numerical tool capable to simulating the inclusion of draining elements in soils. These elements are represented by subhorizontais drains or wells, constituting systems geotechnical widely used in stability of slopes, tunnels and other problems. The implementation was based in the finite elements programs of flow SWMS_2D and SWMS_3D (Simunek e outros, 1994). The proposed formulation considers the equation of flow of the draining element and the numerical strategy of its inclusion by using the method finite elements. A few numerical analyses were carried out aiming at the validation of the proposed algorithm. For the wells, the confined and unconfined cases and in permanent and flow transient conditions have been analyzed, comparing the obtained numerical solutions with the analytical one by Theis (1935) (Freeze, 1979), for water-bearing confined, and one by Neumann (1975), for water-bearing unconfined. For the subhorizontais drains, an analysis methodology is proposed here, taking in to consideration the hydraulical and geometric parameters of a drain element. In this case illustrative examples are presented. The implementation carried out is a simplified one but is should be adequate for the design of geotechnical structures.
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Lele, Suvrat Pratapsinh. "On a class of strain gradient plasticity theories : formulation and numerical implementation". Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43141.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.Includes bibliographical references (p. 247-251).
This study develops strain-gradient theories for isotropic and crystal plasticity. The following four theories were developed and numerically implemented: * A one-dimensional theory to understand the basic nature of strain gradient theories; * A small deformation crystal plasticity theory; * A small deformation theory for isotropic viscoplastic materials; and, * A large deformation theory for isotropic viscoplastic materials. The theories are based on: (i) microstresses consistent with microforce balances; (ii) a mechanical version of the two laws of thermodynamics for isothermal conditions, that includes via the microstresses the work performed during viscoplastic flow; and (iii) a thermodynamically consistent constitutive theory. The microscopic force balance, when augmented by constitutive relations for the microscopic stresses, results in a nonlocal flow rule in the form of a second-order partial differential equation for the plastic strain. The flow rule, being nonlocal, requires microscopic boundary conditions. The theories are numerically implemented by writing a user-element for a commercial finite element program. Using this numerical capability, the major characteristics of the theory are revealed by studying the standard problem of simple shear of a constrained plate. Additional boundary-value problems representing idealized two-dimensional models of grain-size-strengthening and dispersion-strengthening of metallic materials are also studied using the small deformation version of the isotropic theory. For problems that do not involve boundary conditions on plastic strain, the flow rule may be considered to be in conventional form, with additional strengthening terms, instead of a partial differential equation. The finite deformation version of the isotropic theory is numerically implemented by writing a user material model for this approach. Using this implementation, the problems of stabilization of widths of localization shear bands, strengthening in pure bending, and depth dependence of micro and nano-indentation hardness are studied.
by Suvrat Pratapsinh Lele.
Ph.D.
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POWERS, LYNN MARIE. "Mechanical Behavior of Ceramics at High Temperatures: Constitutive Modeling and Numerical Implementation". Case Western Reserve University School of Graduate Studies / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=case1149816510.
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Baroud, Rawad. "Development and implementation of numerical models for the study of multilayered plates". Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1084/document.
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L’utilisation des multicouches prend de plus en plus d’ampleur dans le domaine des sciences de l’ingénieur, tout d’abord dans l’industrie, et plus récemment de plus en plus en Génie Civil. Qu’il s’agisse de complexes mêlant des polymères, du bois ou du béton, des efforts importants sont nécessaires pour la modélisation fine de ce type de matériaux. En effet, des phénomènes induits par l’anisotropie et l’hétérogénéité sont associés à ces multi-matériaux : effets de bords, dilatations thermiques différentielles, délaminages/décollements ou non linéarités de type viscosité, endommagement, plasticité dans les couches ou aux interfaces. Parmi les modèles proposés dans la littérature, on trouve par exemple des modèles monocouche équivalente ou de type "Layerwise" (une cinématique par couche). Appartenant à cette deuxième catégorie, des modèles ont été développés depuis quelques années dans le laboratoire Navier et permettent une description suffisamment fine pour aborder les problématiques spécifiques citées plus haut tout en conservant un caractère opératoire certain. En introduisant des efforts d’interfaces comme des efforts généralisés du modèle, ces approches ont montré leur efficacité vis-à-vis de la représentation des détails au niveau inter- et intra-couches. Il est alors aisé de proposer des comportements et des critères d’interfaces et d’être efficace pour la modélisation du délaminage ou décollement, phénomène très présent dans les composites multicouches assemblés et collés. Par conséquent, un programme éléments finis MPFEAP a été développé dans le laboratoire Navier. Le modèle a également été introduit sous la forme d’un User Element dans ABAQUS, dans sa forme la plus simple (interfaces parfaites).Un nouveau model layerwise est proposé dans ce mémoire pour les plaques multicouches, appelé "Statically Compatible Layerwise Stresses with first-order membrane stress approximations per layer in thickness direction" SCLS1. Le modèle est conforme aux équations d’équilibre 3D ainsi qu’aux conditions aux limites de bord libre. En outre, une version raffinée du nouveau modèle est obtenu en introduisant plusieurs couches mathématiques par couche physique. Le nouveau modèle a été mis en œuvre dans une nouvelle version du code éléments finis MPFEAP.En parallèle, un programme d’éléments finis basé sur la théorie Bending-Gradient développée dans le laboratoire Navier est proposé ici. Le modèle est une nouvelle théorie de plaque épaisse chargée hors-plan où les inconnues statiques sont celles de la théorie Love-Kirchhoff, à laquelle six composantes sont ajoutées représentant le gradient du moment de flexion. La théorie Bending- Gradient est obtenue à partir de la théorie Generalized-Reissner: cette dernière implique quinze degrés de liberté cinématiques, huit d’entre eux étant lié uniquement à la déformation de Poisson hors-plan, et donc l’idée principale de la théorie de plaque Bending-Gradient est de simplifier la théorie Generalized-Reissner en réglant ces huit d.o.f. à zéro et de négliger la contribution de la contrainte normale σ33 dans l’équation constitutive du modèle de plaque. Un programme éléments finis appelé BGFEAP a été développé pour la mise en œuvre de l’élément de Bending-Gradient. Un User Element dans Abaqus a été aussi développé pour la théorie Bending-GradientThe use of multilayer is becoming increasingly important in the field of engineering, first in the industry, and more recently more and more in Civil Engineering. Whether complex blend of polymers, wood or concrete, significant efforts are required for accurate modeling of such materials. Indeed, phenomena induced anisotropy and heterogeneity are associated with these multi-material: edge effects, differential thermal expansion, delamination/detachment or nonlinearities viscosity type damage, plasticity in layers or interfaces. Among the models proposed in the literature, we found for example equivalent monolayer model or of "LayerWise" type (a kinematic per layer). Belonging to the second category, models have been developed in recent years in Navier allow a sufficiently detailed description to address specific issues mentioned above while maintaining a surgical nature. By introducing interface forces as generalized forces of the model, these approaches have demonstrated their effectiveness vis-à-vis the representation of details at inter- and intra-layers. It is then easy to offer behaviors and interfaces criteria and to be effective for modeling delamination or detachment, phenomenom very present in multilayered composites assembled and glued together. Therefore, a finite element program MPFEAP was developed in Navier laboratory. The model was also introduced as a User Element in ABAQUS, in its simplest form (perfect interfaces).A new layerwise model for multilayered plates is proposed in this dissertation, named Statically Compatible Layerwise Stresses with first-order membrane stress approximations per layer in thickness direction SCLS1. The model complies exactly with the 3D equilibrium equations and the free-edge boundary conditions. Also, a refined version of the new model is obtained by introducing several mathematical layers per physical layer. The new model has been implemented in a new version of the in-house finite element code MPFEAP.In parallel, a finite element program based on the Bending-Gradient theory which was developed in Navier laboratory, is proposed here. The model is a new plate theory for out-of-plane loaded thick plates where the static unknowns are those of the Love-Kirchhoff theory, to which six components are added representing the gradient of the bending moment. The Bending-Gradient theory is obtained from the Generalized-Reissner theory: the Generalized-Reissner theory involves fifteen kinematic degrees of freedom, eight of them being related only to out-of-plane Poisson’s distortion and thus, the main idea of the Bending-Gradient plate theory is to simplify the Generalized-Reissner theory by setting these eight d.o.f. to zero and to neglect the contribution of the normal stress σ33 in the plate model constitutive equation. A finite element program called BGFEAP has been developed for the implementation of the Bending-Gradient element. A User Element in Abaqus was also developed for the Bending-Gradient theory
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Lee, Chungwon. "Combined traffic signal control and traffic assignment : algorithms, implementation and numerical results /". Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.
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D'Ambrosio, Raffaele. "Highly Stable Multistage Numerical Methods for Functional Equations: Theory and Implementation Issues". Doctoral thesis, Universita degli studi di Salerno, 2010. http://hdl.handle.net/10556/112.
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2008-2009Functional equations provide the best and most natural way to describe evolution in time and space, also in presence of memory. In fact, the spread of diseases, the growth of biological populations, the brain dynamics, elasticity and plasticity, heat conduction, fluid dynamics, scattering theory, seismology, biomechanics, game theory, control, queuing theory, design of electronic filters and many other problems from physics, chemistry, pharmacology, medicine, economics can be modelled through systems of functional equations, such as Ordinary Differential Equations (ODEs) and Volterra Integral Equations (VIEs). For instance, ODEs based models can be found in the context of evolution of biological populations, mathematical models in physiology and medicine, such as oncogenesis and spread of infections and diseases, economical sciences, analysis of signals. Concerning VIEs based models, the following books and review papers contain sections devoted to this subject in the physical and biological sciences: Brunner, Agarwal and O’Regan, Corduneanu and Sandberg, Zhao. Most of these also include extensive lists of references. Regarding some specific applications of VIEs, they are for example models of population dynamics and spread of epidemics, wave problems, fluido-dynamics, contact problems,electromagnetic signals.
Arizona State University
VIII n.s.
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Spiezia, Nicolo. "Multiphase material modelling in finite deformations: theoretical aspects, numerical implementation and applications". Doctoral thesis, Università degli studi di Padova, 2015. http://hdl.handle.net/11577/3423917.
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Multiphase materials are of primary relevance in many disciplines in engineering and science. They consist of a porous solid skeleton, whose pores are filled by one or more fluid phases, such as water, air, gas, oil etc. The relevant number of applications involving multiphase material motivated the development of several theoretical models and numerical procedures to describe the coupled behavior between the different phases. Most of these models, based on the formulation of the balance laws for the coexisting phases, rely upon the assumption of small strains, which is a simplifying but restrictive hypothesis for several applications.
The aim of this thesis is to investigate the theoretical aspects and the numerical solutions of a multiphase material undergoing large elastoplastic strains, taking into account the fully coupling between the solid and the fluid phases. The essential idea of the model consists in imposing the balance laws for the two (or more) phases in the current deformed configuration, and to solve it numerically with a finite element method. To deal with elastoplasticity at finite strains, the formulation adopts the multiplicative decomposition of the deformation gradient.
The developed numerical model has been applied, in particular, to assess the stability of a horizontal wellbore drilled through a high porous rock formation, quantifying the stress and strain distribution, the evolution of the plastic deformations and the propagation of band of intense deformation. To capture both the shear-enhanced compaction and the shear-induced dilation characteristic of porous rock, an innovative elastoplastic constitutive model has been derived, endowed with a linear and elliptical yield surface that intersect smoothly. The results of the simulations show the capability of the finite deformations coupled approach to simulate the whole process.I materiali multifase sono di primaria importanza in molte discipline dell’ingegneria e della scienza. Essi sono costituiti da uno scheletro solido poroso, i cui pori sono riempiti da una o più fluidi, ad esempio acqua, aria, gas, petrolio, etc. Il vasto campo di applicazione dei materiali multifase ha motivato lo sviluppo di diversi modelli teorici e procedure numeriche per descrivere il comportamento accoppiato fra le diverse fasi. La maggior parte di questi modelli, basati sulla formulazione delle leggi di bilancio per le differenti fasi coesistenti, si basano sul presupposto di piccole deformazioni, ipotesi che comporta una semplificazione dei modelli ma allo stesso tempo risulta essere restrittiva per diverse applicazioni. Lo scopo di questa tesi è indagare gli aspetti teorici e le soluzioni numeriche di un materiale multifase che subisce grandi deformazioni elastoplasticche, tenendo conto del completo accoppiamento tra la fase solida e la fase fluida. L’idea essenziale del modello consiste nell’imporre le leggi di bilancio per le due (o più) fasi nella configurazione corrente deformata, e poi risolvere tali equazioni numericamente con un metodo agli elementi finiti. Per quanto concerne l’elastoplasticità a deformazioni finite, la formulazione adotta la decomposizione moltiplicativa del gradiente di deformazione. Il modello numerico sviluppato è stato applicato, in particolare, per valutare la stabilità di un pozzo perforato orizzontalmente attraverso una formazione rocciosa altamente porosa, per quantificare la distribuzione delle tensioni e delle deformazioni, per descrivere l’evoluzione delle deformazioni plastiche e la propagazione di bande di deformazione. Per cogliere tanto il fenomeno di compattazione e di dilatazione plastica, caratteristico di rocce ad alta porosità, è stato sviluppato un innovativo modello costitutivo elastoplastico, dotato di una superficie lineare e di una superficie ellittica che si intersecano mantenendo la derivabilità in ogni punto. I risultati delle simulazioni mostrano la capacità dell’approccio a grandi deformazioni per simulare l’intero processo accoppiato.
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Rosato, Daniele. "On the formulation and numerical implementation of dissipative electro-mechanics at large strains". Stuttgart Inst. für Mechanik (Bauwesen), 2010. http://d-nb.info/1003206476/34.
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Livings, William T. "Fleet Numerical Oceanography Center software development standards: an implementation of DOD-STD-2167A". Thesis, Monterey, California. Naval Postgraduate School, 1989. http://hdl.handle.net/10945/25949.
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Hakim, Layal. "Numerical implementation of a cohesive zone model for time and history dependent materials". Thesis, Brunel University, 2014. http://bura.brunel.ac.uk/handle/2438/8556.
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A cohesive zone model approach is used in order to study the behaviour of cracks in elasto-plastic materials. The cohesive zone model being studied is time-dependent, unlike standard cohesive zone models in elasto-plasticity. The stress distribution over the cohesive zone is related to the normalised equivalent stress functional, and is expressed in the form of an Abel-type integral equation. During the stationary crack stage as well as the propagating crack stage, the aim is to study the behaviour of the cohesive zone length with respect to time as well as the crack tip opening. To aid accomplishing this aim, the stress intensity factor was set to zero at the cohesive zone tip. As well as other material parameters, the external applied load participates in the model equations. We will consider two cases for the external load, namely the case when this load is constant in time, and the case when this load behaves linearly with time. We will implement numerical schemes to obtain the crack growth as well as the cohesive zone growth with respect to time for both the elastic case and the visco-elastic case while considering different sets of parameters. The numerical convergence rates are obtained for each of the problems solved. This justifies the suitability of the numerical schemes used.
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Hill, Jonathan. "Efficient Implementation of Mesh Generation and FDTD Simulation of Electromagnetic Fields". Digital WPI, 1999. https://digitalcommons.wpi.edu/etd-theses/1055.
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"This thesis presents an implementation of the Finite Difference Time Domain (FDTD) method on a massively parallel computer system, for the analysis of electromagnetic phenomenon. In addition, the implementation of an efficient mesh generator is also presented. For this research we selected the MasPar system, as it is a relatively low cost, reliable, high performance computer system. In this thesis we are primarily concerned with the selection of an efficient algorithm for each of the programs written for our selected application, and devising clever ways to make the best use of the MasPar system. This thesis has a large emphasis on examining the application performance."
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Banks, Nicola E. "Insights from the parallel implementation of efficient algorithms for the fractional calculus". Thesis, University of Chester, 2015. http://hdl.handle.net/10034/613841.
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This thesis concerns the development of parallel algorithms to solve fractional differential equations using a numerical approach. The methodology adopted is to adapt existing numerical schemes and to develop prototype parallel programs using the MatLab Parallel Computing Toolbox (MPCT). The approach is to build on existing insights from parallel implementation of ordinary differential equations methods and to test a range of potential candidates for parallel implementation in the fractional case. As a consequence of the work, new insights on the use of MPCT for prototyping are presented, alongside conclusions and algorithms for the effective implementation of parallel methods for the fractional calculus. The principal parallel approaches considered in the work include: - A Runge-Kutta Method for Ordinary Differential Equations including the application of an adapted Richardson Extrapolation Scheme - An implementation of the Diethelm-Chern Algorithm for Fractional Differential Equations - A parallel version of the well-established Fractional Adams Method for Fractional Differential Equations - The adaptation for parallel implementation of Lubich's Fractional Multistep Method for Fractional Differential Equations An important aspect of the work is an improved understanding of the comparative diffi culty of using MPCT for obtaining fair comparisons of parallel implementation. We present details of experimental results which are not satisfactory, and we explain how the problems may be overcome to give meaningful experimental results. Therefore, an important aspect of the conclusions of this work is the advice for other users of MPCT who may be planning to use the package as a prototyping tool for parallel algorithm development: by understanding how implicit multithreading operates, controls can be put in place to allow like-for-like performance comparisons between sequential and parallel programs.
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Tyler, Jonathan. "Analysis and implementation of high-order compact finite difference schemes /". Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2177.pdf.
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Chen, Chengkun. "Development and implementation of novel numerical techniques for integrated optics and microwave planar structures". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0017/MQ57097.pdf.
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Briggs, Victoria Alice 1974. "Numerical modeling of borehole acoustics : parallel implementation of a loggin-while-drilling (LWD) model". Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/58061.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2000.Includes bibliographical references (p. 41-42).
A finite difference code is used to investigate acoustic waves in a borehole environment. The wave response to a logging-while-drilling (LWD) geometry is modeled in a fast formation. Helical waves circling the tool are shown to asymptote to the Stoneley wave velocity, giving confirmation of the fluid velocity in the borehole. Parameter studies for simpler borehole geometries show that the Stoneley wave, in soft formations where no shear arrival is present, can be used to invert for the shear velocity of the rock. A Beowulf parallel computer is used to implement the finite difference code showing the efficiency of cluster computing in a discretized space.
by Victoria Alice Briggs.
S.M.
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Rödiger, Jasper. "Time-Frequency Quantum Key Distribution: Numerical Assessment and Implementation over a Free-Space Link". Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21046.
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Die Quantenschlüsselverteilung (QKD), die erste anwendbare Quantentechnologie, verspricht informationstheoretisch sichere Kommunikation. In der vorliegenden Arbeit wurde das Zeit-Frequenz (TF)-QKD-Protokoll untersucht, das Zeit und Frequenz, nämlich Puls-Positionsmodulation (PPM) im Zeitbereich und Frequenzumtastung (FSK) im Frequenzbereich als die beiden komplementären Basen verwendet. Seine Sicherheit beruht den Quanteneigenschaften von Licht und auf der Zeit-Frequenz-Unschärferelation.
TF-QKD kann mit größtenteils Standard-Telekommunikationstechnologie im 1550-nm-Band implementiert werden. Die PPM-Basis kann mit Modulatoren und die FSK-Basis mit Hilfe der Wellenlängenmultiplex-Technologie realisiert werden. Das TF-QKD-Protokoll ist in der Lage, ein beliebig großes Alphabet bereitzustellen, was mehr als 1 bit/Photon ermöglicht. Darüber hinaus ist es robust gegenüber athmosphärischen Störungen und somit für die Übertragung über den Freiraumkanal geeignet.
In der vorliegenden Arbeit wird das TF-QKD-Protokoll theoretisch bewertet, mit Standardkomponenten für 1 bit/Photon implementiert und die Freiraumübertragung mit optischem Tracking über eine 388 m Teststrecke wird bei Tageslicht demonstriert. Unter Verwendung der vorhandenen Komponenten konnte eine sichere Schlüsselrate von 364 kbit/s back-to-back und 9 kbit/s über den Freiraumkanal demonstriert werden.Quantum key distribution (QKD), the first applicable quantum technology, promises information theoretically secure communication. In the presented work the time-frequency (TF)-QKD protocol was examined, which uses time and frequency, namely pulse position modulation (PPM) in the time domain and frequency shift keying (FSK) in the frequency domain as the two complementary bases. Its security relies on the quantum properties of light and the time-frequency uncertainty relation. TF-QKD can be implemented mostly with standard telecom-technology in the 1550 nm band. The PPM basis can be implemented with modulators and the FSK basis with help of wavelength-division multiplexing technology. The TF-QKD protocol is capable of providing an arbitrarily large alphabet enabling more than 1 bit/photon. Moreover, it is robust in the atmosphere making it suitable for transmission over the free-space channel. In the present work the TF-QKD protocol is assessed theoretically, implemented with off-the-shelf components for 1 bit/photon and free-space transmission with optical tracking over a 388 m testbed is demonstrated in daylight. Using components at hand, secret key rates of 364 kbit/s back-to-back and 9 kbit/s over the free-space channel could be demonstrated.
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Hedendal, Daniel. "Towards a relativistically covariant many-body perturbation theory : with numerical implementation to helium-like ions /". Göteborg : Department of Physics, University of Gothenburg, 2010. http://hdl.handle.net/2077/22083.
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Robertson, Eric D. "Verification, validation, and implementation of numerical methods and models for OpenFOAM 2.0 for incompressible flow". Thesis, Mississippi State University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1596091.
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A comprehensive survey of available numerical methods and models was performed on the open source computational fluid dynamics solver OpenFOAM version 2.0 for incompressible turbulent bluff body flows. Numerical methods are illuminated using source code for side-by-side comparison. For validation, the accuracy of flow predictions over a sphere in the subcritical regime and delta wing with sharp leading edge is assessed. Solutions show mostly good agreement with experimental data and data obtained from commercial software. A demonstration of the numerical implementation of a dynamic hybrid RANS/LES framework is also presented, including results from test studies.
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Shuler, Harrey Jeong. "Recovery of the local gravity field by spherical regularization wavelets approximation and its numerical implementation". Thesis, The University of Texas at Austin, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3615225.
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As an alternative to spherical harmonics in modeling the gravity field of the Earth, we built a multiresolution gravity model by employing spherical regularization wavelets in solving the inverse problem, i.e. downward propagation of the gravity signal to the Earth's surface. Scale discrete Tikhonov spherical regularization scaling function and wavelet packets were used to decompose and reconstruct the signal. We recovered the local gravity anomaly using only localized gravity measurements at the observing satellite's altitude of 300 km. When the upward continued gravity anomaly to the satellite altitude with a resolution 0.5° was used as simulated measurement inputs, our model could recover the local surface gravity anomaly at a spatial resolution of 1° with an RMS error between 1 and 10 mGal, depending on the topography of the gravity field. Our study of the effect of varying the data volume and altering the maximum degree of Legendre polynomials on the accuracy of the recovered gravity solution suggests that the short wavelength signals and the regions with high magnitude gravity gradients respond more strongly to such changes. When tested with simulated SGG measurements, i.e. the second order radial derivative of the gravity anomaly, at an altitude of 300 km with a 0.7° spatial resolution as input data, our model could obtain the gravity anomaly with an RMS error of 1 ~ 7 mGal at a surface resolution of 0.7° (< 80 km). The study of the impact of measurement noise on the recovered gravity anomaly implies that the solutions from SGG measurements are less susceptible to measurement errors than those recovered from the upward continued gravity anomaly, indicating that the SGG type mission such as GOCE would be an ideal choice for implementing our model. Our simulation results demonstrate the model's potential in determining the local gravity field at a finer scale than could be achieved through spherical harmonics, i.e. less than 100 km, with excellent performance in edge detection.
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Dias, dos Santos Jose. "Implementation and comparison of numerical algorithms for the solution of linear systems using transputer networks". Thesis, University of Kent, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.256255.
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Oyola, Mayra I. "Implementation of a Global Dust Physical Sea Surface Temperature Retrieval For Numerical Weather Prediction Applications". Thesis, Howard University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10188977.
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This works presents the results for the first study to ever attempt to analyze the full potential and limitations of incorporating aerosols within a truly physical SST retrieval for operational weather forecasting purposes. This is accomplished through the application of a satellite sea surface temperature (SST) physical retrieval for satellite split-window and hyperspectral infrared (IR) sensors that allows a better representation of the atmospheric state under aerosol-laden conditions. The new algorithm includes 1) accurate specification of the surface emissivity that characterizes the surface leaving radiance and 2) transmittance and physical characterization of the atmosphere by using the Community Radiative transfer model (CRTM). This project includes application of the NEMS-Global Forecasting System Aerosol Component (NGAC) fields, which corresponds to the first global interactive atmosphere-aerosol forecast system ever implemented at NOAA’s National Center for Environmental Prediction (NCEP).
A number of limiting factors were identified by analysing brightness temperatures and SST outputs biases as a function of latitude, zenith angle, wind and moisture for cases in January and November 2013. SST ouputs are validated against a bulk SST (Reynolds SST) and a parameterized SST derived from operational products and partly against observed measurements from the eastern Atlantic Ocean, which is dominated by Saharan dust throughout most of the year and that is also a genesis region for Atlantic tropical cyclones. These observations are obtained from the NOAA Aerosols and Ocean Science Expeditions (AEROSE). The improved physical SST methodology has the potential to allow for improved representation of the geophysical state under dust-laden conditions.
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Karantzoulis, Nikolaos. "Development and implementation of inelastic material models for use in FEMDEM numerical methods with applications". Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/58998.
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The combined Finite–Discrete Element Method (FEMDEM) is one of the most versatile numerical frameworks for the mechanical analysis of multi-body industrial applications. Currently, the inclusion of only elastic and brittle material models limits the problems that can be realistically simulated. This new work focuses on expanding the capabilities of existing FEMDEM codes in order to include inelastic material models successfully. After describing and implementing the appropriate theoretical and numerical framework for elasto-plasticity, a thorough numerical verification analysis is presented. Test cases, varying from simple one-dimensional quasi-static problems through to fully three-dimensional impact analysis, are explored to illustrate the stability, accuracy and robustness of the inelastic behaviour implemented. The extension of this plasticity implementation to finite deformations is then discussed. The ability of the extended simulation tool to capture large strain non-linear phenomena is then numerically demonstrated with the successful analysis of two benchmark problems: (a) the high-speed impact of a copper rod against a wall; (b) the unconfined uniaxial compression of a cylinder with Mohr-Coulomb plasticity. To explore the potential range of the new model, a complete case study to simulate concrete crushing behaviour during an impact test is performed. A simple experimental setup is designed to investigate steel-to-concrete inelastic collisions focusing on the energy losses via the coefficient of restitution. The processed experimental results, combined with concrete-characterisation tests are used to calibrate a two-parameter Mohr-Coulomb material model via parametric numerical analysis. In order to overcome current limitations, a generalised piece-wise Drucker-Prager plasticity model to accommodate non-linear material plasticity behaviour is developed and corresponding return-mapping equations are discussed in detail. The foregoing extension to large strain plasticity of the in-house FEMDEM multi-body simulator, Solidity, is discussed in a more general context by reviewing recent FEMDEM development and application research being undertaken at Imperial College. Finally, this work is put into the overall context of the multi-physics research plans by providing preliminary analysis results for two industrial applications: (a) concrete armour units impacts, (b) powder compaction.
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Poli, Arianna <1990>. "Dynamic analyses of geotechnical problems using advanced constitutive formulations: soil parameter calibration and numerical implementation". Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amsdottorato.unibo.it/8977/1/Poli_Arianna_tesi.pdf.
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The doctoral research has focused on an accurate study of granular soil behaviour in static and seismic conditions, with special reference to seismic-induced phenomena such as liquefaction and lateral spreading whose evidences have been observed during the 2012 Emilia earthquake. The basic aim of the study has been to develop an innovative numerical tool for reproducing the mechanical response of silty-sand soils under different loading and drainage conditions adopting an advanced constitutive model, which could be calibrated from tests that are routinely performed in geotechnical laboratory. Thus, an experimental testing programme, including triaxial tests, standard and K0-cell oedometer tests, has been carried out on a number of sandy and silty samples extracted from the subsoil of Scortichino (Emilia-Romagna, Northern Italy), a village struck by the 2012 seismic sequence. Therefore, the experimental results have been interpreted taking a Generalized Plasticity-based model for sands as reference constitutive framework. In particular, starting from the existing formulation devised by Pastor et al. (1990) and later extended by Tonni et al. (2006) and Cola et al. (2008), a few modifications have been introduced to the original constitutive equations in order to improve the predictive capability. An in-depth calibration study has been performed and an effective procedure to obtain the model parameters has been defined. For this purpose, a MATLAB numerical routine has been developed. Finally, the constitutive equations have been implemented in a 2D FE code (GeHoMADRID) and a detailed numerical model of the riverbank has been realized in order to perform advanced dynamic analyses and to study both the stress-strain behaviour and the seismic-induced effects within the investigated granular deposits during the 2012 Emilia earthquake.
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Islam, Mohammad Sayful. "Implementation and testing of techniques for improving the performance of Richards' equation solvers and the handling of heterogeneous soils". Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3425273.
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Efficient, robust simulation of groundwater flow in the unsaturated zone remains computationally expensive, especially for problems characterized by sharp fronts in both space and time. Standard approaches that employ uniform spatial and temporal discretizations for the numerical solution of these problems lead to inefficient and expensive simulations. Accurate solution of the pressure-head form of Richards' equation is very difficult using standard time integration methods, because the mass balance errors grow unless very small time steps are used in the time integration process. Richards' equation may be solved for many problems more economically and robustly with variable time step size instead of constant time step size. But variable step-size methods applied to date have relied upon empirical approaches to control step size which do not explicitly control truncation error of the solution. In the first part of this thesis, we solve Richards' equation using the method of lines with a finite difference approach. We show how a differential algebraic equation implementation of the method of lines can give solutions to Richards' equation that are accurate, have good mass balance properties, and are more economical for a wide range of solution accuracy. We have implemented the method of lines using the higher order time integration ode solver ode15s to (i) assure robustness for difficult nonlinear problems and computational efficiency; (ii) develop high order adaptive methods for the time discretization taking into account the different time scales that may appear in the process; (iii) investigate the advantage of using higher-order methods in time. The numerical results demonstrate that the proposed method provides a robust and efficientalternative to standard approaches for simulating variably saturated flow in one spatial dimension.
In the 2nd part of the thesis, we to investigate the convergence and mass balance behavior in Richards' equation-based solvers. As hydrological models become increasingly sophisticated (e.g., coupling with various meteorological, ecological, or biogeochemical components) and are applied in ever more computationally demanding contexts (e.g., the many realizations that are typically generated in parameter estimation, uncertainty analysis, data assimilation, or scenario studies), the need for robust, accurate, and efficient codes is greater than ever. The Richards equation for subsurface flow is highly nonlinear and requires iterative schemes for its solution. These schemes have been the subject of much research over the past two decades, but an effective all-purpose algorithm has thus far proven elusive. Ideally, rapid (quadratic as opposed to linear) and global (insensitive to initial guess) convergence is sought, in addition to applicability over a range of conditions (dry soils, storm-interstorm simulations, geological heterogeneity, 3D domains with complex boundary conditions, etc). Richards’ equation can be mathematically formulated and numerically discretized in a variety of manners, and the specific form and scheme chosen will affect the mass balance behavior of the model. We implement and test a promising nested Newton-type algorithm for solving Richards' equation. In the current state of the art, the Picard iteration method is widely used for solving the nonlinear equation governing flow in variably saturated porous media because this method is simple to code and computationally cheap. But the convergence is slow and sometimes fails. On the other hand, the Newton method is more complex and expensive than Picard. As a result the Picard method is more attractive than Newton. However, especially for strongly nonlinear flow problems, the robustness and higher rate of convergence makes Newton an attractive alternative in some cases. In this work the Picard and Newton schemes are compared with results of a nested Newton-type algorithm. Three test cases are presented and each problem is solved over a wide range of vertical discretization. The results highlight the different aspects of the performance of the iterative methods and the different factors that can affect their convergence and efficiency, including problem size, spatial and temporal discretization, convergence error norm, mass lumping, time weighting, conductivity, moisture content characteristics, and boundary conditions. It is suggested that nested Newton-type methods can be effectively implemented and used alongside Picard and Newton and numerical models of Richards' equation.
In the final part of the thesis, we studied the performance of a lookup table option, as an alternative to analytical calculation, for evaluating the nonlinear soil characteristics needed in the Picard and Newton schemes. This assessment is conducted for the CATHY (CATchment Hydrology) 3D Richards-based subsurface flow solver. The lookup table method can be a cost-effective alternative to analytical evaluation in the case of heterogeneous soils, but it has not been examined in detail in the hydrological modeling literature. Two layered soil test problems are considered, and the robustness and accuracy of the lookup table method are assessed for uniform and nonuniform distributions of lookup points in the soil retention curvesSimulazioni robuste ed efficienti del flusso dell’acqua in suolo insaturo è ancora un problema computazionale di difficile soluzione, in particolare nei casi di infiltrazione in suolo relativamente secco per la presenza di grandi gradienti nella soluzione approssimata che esaltano le nonlinearità e rendono difficile la trattazione numerica. Gli approcci tradizionali che impiegano discretizzazioni spaziali e temporali uniformi sono inefficienti e computazionalmente assai costosi, oltre che essere spesso affetti da grandi errori nella conservazione discrete della massa. Algoritmi temporalmente adattativi sono stati proposti ma sono ancora computazionalmente inefficienti in particolare in presenza di forzanti esterne ad alta variabilità, quali quelle causate dai flussi di precipitazione. Nella prima parte di questa tesi viene sperimentato l’approccio risolutivo che impiega tali algoritmi tramite il metodo delle linee (MOL) utilizzando solutori di tipo DAE (DifferentialAlgebraic Equation). Si verifica sperimentalmente che questo modo di procedure può essere preferibile a tecniche a passo fisso per alcuni casi test. Tale approccio, basato su solutori temporali di alto grado di accuratezza, quando applicabile, si dimostra efficiente e competitivo rispetto a metodi più tradizionali, mantenendo buone proprietà di robustezza e conservazione della massa, quando si utilizzino approcci mono-dimensionali. Nella seconda parte della tesi ci si focalizza più direttamente nelle proprietà di convergenza e conservazione della massa di metodi recentemente proposti in letteratura applicati a problemi eterogenei e multidimensionali. La moderna applicazione di modelli idrologici vede un arricchirsi dei processi considerati accoppiando l’equazione di Richards a modelli diversi derivanti da applicazioni metereologiche, ecologiche e bio-geo-chimiche, con la conseguente richiesta di metodi numerici più efficienti e robusti. Idealmente, si richiede a questi schemi una convergenza rapida, possibilmente quadratica, e globale in tutte le circostanze (e.g., suoli aridi, simulazioni “storm-interstorm”, grandi eterogeneità, condizioni al contorno nonlineari, eccetera). Anche il tipo di formulazione matematica dell’equazione di Richards nel continuo (ad esempio in forma completamente conservativa oppure semi-conservativa) determina diverse efficienze dei diversi metodi in funzione delle condizioni forzanti. Per questi motivi, viene implementato e testato in condizioni “estreme” un algoritmo basato sull’applicazione annidata del metodo di Newton e proposto recentemente nella letteratura. La verifica viene fatta per confronto con metodi di Newton e Newton-Picard più tradizionali su tre test sintetici ma realistici e probanti. Per ciascun test si verifica la robustezza dei diversi schemi a variazioni di griglia sia temporale che spaziale, e si confrontano i risultati in termini di velocità di convergenza, e quindi efficienza numerica. I risultati suggeriscono che il nuovo metodo “nested-Newton” risulta assai competitivo dimostrando ottime proprietà di convergenza anche nei test più difficili. Infine, l’ultima parte della tesi è volta a verificare l’efficienza computazionale nell’uso negli schemi di Picard e Newton di tecniche di “look-up” che discretizzano le curve caratteristiche delle relazioni pressione-saturazione (responsabili della nonlinearità nell’equazione di Richards) utilizzando il solutore CATHY (CATchmentHYdrology). I risultati mostrano che l’uso di tabelle di “look-up” migliora l’efficienza computazionale dei metodi alla Newton tradizionali in casi test omogenei e eterogenei rispetto ai metodi analitici qualora le curve caratteristiche possano essere accuratamente descritte da un numero di punti limitato
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Anderson, Lauren C. "Isolation and implementation of the dynamical core from the German Weather Service's numerical weather prediction model". Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1446091.
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Rosato, Daniele [Verfasser]. "On the formulation and numerical implementation of dissipative electro-mechanics at large strains / von Daniele Rosato". Stuttgart : Inst. für Mechanik (Bauwesen), 2010. http://d-nb.info/1003206476/34.
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Mbiakop, Armel. "Nonlinear homogenization in porous creeping single crystals: Modeling, numerical implementation and applications to fracture and fatigue". Palaiseau, Ecole polytechnique, 2015. https://theses.hal.science/tel-01235253/document.
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Skjerven, Brian M. "A parallel implementation of an agent-based brain tumor model". Link to electronic thesis, 2007. http://www.wpi.edu/Pubs/ETD/Available/etd-060507-172337/.
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Thesis (M.S.) -- Worcester Polytechnic Institute.Keywords: Visualization; Numerical analysis; Computational biology; Scientific computation; High-performance computing. Includes bibliographical references (p.19).
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Garcia, Gonzalez Jesus. "Numerical analysis of fluid motion at low Reynolds numbers". Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/numerical-analysis-of-fluid-motion-at-low-reynolds-numbers(4cf30194-0155-439d-879a-c49787549e8c).html.
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At low Reynolds number flows, the effect of inertia becomes negligible and the fluid motion is dominated by the effect of viscous forces. Understanding of the behaviour of low Reynolds number flows underpins the prediction of the motion of microorganisms and particle sedimentation as well as the development of micro-robots that could potentially swim inside the human body to perform targeted drug/cell delivery and non-invasive microsurgery. The work in this thesis focuses on developing an understanding in the mathematical analysis of objects moving at low Reynolds numbers. A boundary element implementation of the Method of regularized Stokeslets (MRS) is applied to analyse the low Reynolds number flow field around an object of simple shape (sphere and cube). It also showed that the results obtained by a boundary element implementation for an unbounded cube, where singularities are presented in the corners of the cube, agrees with more complex solutions methods such as a GBEM and FEM.A methodology for analysing the effect of walls by locating collocation points on the surface of the walls and the object is presented. First at all, this methodology is validated with a boundary element implementation of the method of images for a sphere at different locations. Then, the method is extended when more than one wall is presented. This methodology is applied to predict the velocity filed of a cube moving in a tow tank at low Reynolds numbers for two different cases with a supporting rod similar to an experimental set-up, and without the supporting rod as in the CFD simulations based on the FVM. The results indicate a good match between CFD and the MRS, and an excellent approximation between the MRS and experimental data from PIV measurements. The drag, thrust and torque generated by helices moving at low Reynolds numbers in an unbounded medium is analysed by the resistive force theory, a slender body theory, and a boundary element method of the MRS. The results show that the resistive force theory predict accurately the drag, thrust and torque of moving helices when the resistive force coefficients are calculated from a slender body theory approximation by calculating independently the resistive force coefficients for translation and rotation, because it is observed that the resistive force coefficients depend also of the nature of motion. Moreover, the thrust generated by helices of different pitch angles is analysed calculated by a CFD numerical simulation based on the FVM and a boundary element implementation, an compared with experimental data. The results also show an excellent prediction between the boundary element implementation, the CFD results and the experimental data. Finally, a boundary element implementation of the MRS is applied to predict swimming of a biomimetic swimmer that mimics the motion of E.coli bacteria in an unbounded medium. The results are compared with the propulsive velocity and induced angular velocity measurement by recording the motion of the biomimetic swimmer in a square tank. It is observed that special care needs to be taken when the biomimetic swimmer is modelled inside the tank, as there is an apparent increment in the calculate thrust propulsion which does not represent a real situation of the biometic swimmer which propels by a power supply. However, this increment does not represent the condition of the biomimetic swimmer and a suggested methodology based on the solution from an unbounded case and when the swimmer is moving inside the tank is presented. In addition, the prediction of the free-swimming velocity for the biomimetic swimmer agrees with the results obtained by the MRS when the resistive force coefficients are calculated from a SBT implementation. The results obtained in this work have showed that a boundary element implementation of the MRS produces results comparable with more complex numerical implementations such as GBEM, FEM, FVM, and also an excellent agreement with results obtained from experimentation. Therefore, it is a suitable and easy to apply methodology to analyse the motion of swimmers at low Reynolds numbers, such as the biomimetic swimmer modelled in this work.
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Nyamayaro, Takura T. A. "On the design and implementation of a hybrid numerical method for singularly perturbed two-point boundary value problems". University of the Western Cape, 2014. http://hdl.handle.net/11394/4326.
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>Magister Scientiae - MScWith the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these solvers are tailor-made for specific classes of problems. Therefore, more of such must be developed to accompany the growing need for mathematical models that help in the understanding of the contemporary world. This thesis treats two point boundary value singularly perturbed problems. The solution to this type of problem undergoes steep changes in narrow regions (called boundary or internal layer regions) thus rendering the classical numerical procedures inappropriate. To this end, robust numerical methods such as finite difference methods, in particular fitted mesh and fitted operator methods have extensively been used. While the former consists of transforming the continuous problem into a discrete one on a non-uniform mesh, the latter involves a special discretisation of the problem on a uniform mesh and are known to be more accurate. Both classes of methods are suitably designed to accommodate the rapid change(s) in the solution. Quite often, finite difference methods on piece-wise uniform meshes (of Shishkin-type) are adopted. However, methods based on such non-uniform meshes, though layer-resolving, are not easily extendable to higher dimensions. This work aims at investigating the possibility of capitalising on the advantages of both fitted mesh and fitted operator methods. Theoretical results are confirmed by extensive numerical simulations.
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Koldan, Jelena. "Numerical solution of 3-D electromagnetic problems in exploration geophysics and its implementation on massively parallel computers". Doctoral thesis, Universitat Politècnica de Catalunya, 2013. http://hdl.handle.net/10803/130833.
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The growing significance, technical development and employment of electromagnetic (EM) methods in exploration geophysics have led to the increasing need for reliable and fast techniques of interpretation of 3-D EM data sets acquired in complex geological environments. The first and most important step to creating an inversion method is the development of a solver for the forward problem. In order to create an efficient, reliable and practical 3-D EM inversion, it is necessary to have a 3-D EM modelling code that is highly accurate, robust and very fast. This thesis focuses precisely on this crucial and very demanding step to building a 3-D EM interpretation method.
The thesis presents as its main contribution a highly accurate, robust, very fast and extremely scalable numerical method for 3-D EM modelling in geophysics that is based on finite elements (FE) and designed to run on massively parallel computing platforms. Thanks to the fact that the FE approach supports completely unstructured tetrahedral meshes as well as local mesh refinements, the presented solver is able to represent complex geometries of subsurface structures very precisely and thus improve the solution accuracy and avoid misleading artefacts in images. Consequently, it can be successfully used in geological environments of arbitrary geometrical complexities. The parallel implementation of the method, which is based on the domain decomposition and a hybrid MPI-OpenMP scheme, has proved to be highly scalable - the achieved speed-up is close to the linear for more than a thousand processors. Thanks to this, the code is able to deal with extremely large problems, which may have hundreds of millions of degrees of freedom, in a very efficient way. The importance of having this forward-problem solver lies in the fact that it is now possible to create a 3-D EM inversion that can deal with data obtained in extremely complex geological environments in a way that is realistic for practical use in industry. So far, such imaging tool has not been proposed due to a lack of efficient, parallel FE solutions as well as the limitations of efficient solvers based on finite differences.
In addition, the thesis discusses physical, mathematical and numerical aspects and challenges of 3-D EM modelling, which have been studied during my research in order to properly design the presented software for EM field simulations on 3-D areas of the Earth. Through this work, a physical problem formulation based on the secondary Coulomb-gauged EM potentials has been validated, proving that it can be successfully used with the standard nodal FE method to give highly accurate numerical solutions. Also, this work has shown that Krylov subspace iterative methods are the best solution for solving linear systems that arise after FE discretisation of the problem under consideration. More precisely, it has been discovered empirically that the best iterative method for this kind of problems is biconjugate gradient stabilised with an elaborate preconditioner. Since most commonly used preconditioners proved to be either unable to improve the convergence of the implemented solvers to the desired extent, or impractical in the parallel context, I have proposed a preconditioning technique for Krylov methods that is based on algebraic multigrid. Tests for various problems with different conductivity structures and characteristics have shown that the new preconditioner greatly improves the convergence of different Krylov subspace methods, which significantly reduces the total execution time of the program and improves the solution quality. Furthermore, the preconditioner is very practical for parallel implementation. Finally, it has been concluded that there are not any restrictions in employing classical parallel programming models, MPI and OpenMP, for parallelisation of the presented FE solver. Moreover, they have proved to be enough to provide an excellent scalability for it.