Dissertations / Theses: 'Discretization'

1

Yang, Ying. "Discretization for Naive-Bayes learning." Monash University, School of Computer Science and Software Engineering, 2003. http://arrow.monash.edu.au/hdl/1959.1/9393.

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Nucinkis, Daniel. "A discretization of quasiperiodic motion." Thesis, Queen Mary, University of London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265698.

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Böhm, Walter, and Sri Gopal Mohanty. "Discretization of Markovian Queueing Systems." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1990. http://epub.wu.ac.at/140/1/document.pdf.

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Recently it turned out, that discretizing the time in a markovian queueing model makes it possible to apply powerfull combinatorid methods which often yield surprisingly simple answeres to complicated questions. In this paper we show that the continuous time solution of a markovian queueing model may be obtain from the solution of its discrete time analogue by a simple limiting procedure. Under mild regularity conditions these limiting forms can be shown to be the unique solutions of Kolmogorov's backward differential equations. Furthermore some additional methodological results concerning taboo probabilities and first passage densities are obtained. In a final section some examples are given. (author's abstract)
Series: Forschungsberichte / Institut für Statistik

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Sugiyama, Mahito. "Studies on Computational Learning via Discretization." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157472.

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Bauer, David. "Towards Discretization by Piecewise Pseudoholomorphic Curves." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-132065.

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This thesis comprises the study of two moduli spaces of piecewise J-holomorphic curves. The main scheme is to consider a subdivision of the 2-sphere into a collection of small domains and to study collections of J-holomorphic maps into a symplectic manifold. These maps are coupled by Lagrangian boundary conditions. The work can be seen as finding a 2-dimensional analogue of the finite-dimensional path space approximation by piecewise geodesics on a Riemannian manifold (Q,g). For a nice class of target manifolds we consider tangent bundles of Riemannian manifolds and symplectizations of unit tangent bundles. Via polarization they provide a rich set of Lagrangians which can be used to define appropriate boundary value problems for the J-holomorphic pieces. The work focuses on existence theory as a pre-stage to global questions such as combinatorial refinement and the quality of the approximation. The first moduli space of lifted type is defined on a triangulation of the 2-sphere and consists of disks in the tangent bundle whose boundary projects onto geodesic triangles. The second moduli space of punctured type is defined on a circle packing domain and consists of boundary punctured disks in the symplectization of the unit tangent bundle. Their boundary components map into single fibers and at punctures the disks converge to geodesics. The coupling boundary conditions are chosen such that the piecewise problem always is Fredholm of index zero and both moduli spaces only depend on discrete data. For both spaces existence results are established for the J-holomorphic pieces which hold true on a small scale. Each proof employs a version of the implicit function theorem in a different setting. Here the argument for the moduli space of punctured type is more subtle. It rests on a connection to tropical geometry discovered by T. Ekholm for 1-jet spaces. The boundary punctured disks are constructed in the vicinity of explicit Morse flow trees which correspond to the limiting objects under degeneration of the boundary condition.

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Pavlov, Dmitry Marsden Jerrold E. Marsden Jerrold E. Desbrun Mathieu. "Structure-preserving discretization of incompressible fluids /." Diss., Pasadena, Calif. : California Institute of Technology, 2009. http://resolver.caltech.edu/CaltechETD:etd-05222009-125630.

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Wang, Bin, and s3115026@student rmit edu au. "On Discretization of Sliding Mode Control Systems." RMIT University. Electrical and Computer Engineering, 2008. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080822.145013.

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Sliding mode control (SMC) has been successfully applied to many practical control problems due to its attractive features such as invariance to matched uncertainties. The characteristic feature of a continuous-time SMC system is that sliding mode occurs on a prescribed manifold, where switching control is employed to maintain the state on the surface. When a sliding mode is realized, the system exhibits some superior robustness properties with respect to external matched uncertainties. However, the realization of the ideal sliding mode requires switching with an infinite frequency. Control algorithms are now commonly implemented in digital electronics due to the increasingly affordable microprocessor hardware although the essential conceptual framework of the feedback design still remains to be in the continuous-time domain. Discrete sliding mode control has been extensively studied to address some basic questions associated with the sliding mode control of discrete-time systems with relatively low switching frequencies. However, the complex dynamical behaviours due to discretization in continuous-time SMC systems have not yet been fully explored. In this thesis, the discretization behaviours of SMC systems are investigated. In particular, one of the most frequently used discretization schemes for digital controller implementation, the zero-order-holder discretization, is studied. First, single-input SMC systems are discretized, stability and boundary conditions of the digitized SMC systems are derived. Furthermore, some inherent dynamical properties such as periodic phenomenon, of the discretized SMC systems are studied. We also explored the discretization behaviours of the disturbed SMC systems. Their steady-state behaviours are discussed using a symbolic dynamics approach under the constant and periodic matched uncertainties. Next, discretized high-order SMC systems and sliding mode based observers are explored using the same analysis method. At last, the thesis investigates discretization effects on the SMC systems with multiple inputs. Some conditions are first derived for ensuring the

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Chen, Heli. "The quadrature discretization method and its applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/NQ34540.pdf.

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Ho, Colin Kok Meng. "Discretization and defragmentation for decision tree learning." Thesis, University of Essex, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299072.

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ANDRADE, SELENE DIAS RICARDO DE. "A COMPARISON BETWEEN DISCRETIZATION METHODS FOR CONTROLLERS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1999. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=1017@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Esta dissertação apresenta uma comparação entre técnicas de discretização de controladores, considerando diferentes estruturas de controle. Os tipos de sistemas estudados neste trabalho de pesquisa serão sistemas lineares, invariantes no tempo, determinísticos, causais e monovariáveis. O desempenho das técnicas de discretização serão comparados via figuras de mérito tradicionais, considerando os métodos de discretização, as estruturas dos controladores e os tipos de planta habituais (incluindo problemas benchmarch), sob especificações dadas quanto aos regimes permanente e transiente.
This essay proposes a comparison between techniques of controllers´ discretization considering different controlling structures. The types of systems studied in this research will be linear systems, time-invariant, deterministic, casual and single-variable. The performance of discretization techniques will be compared through figures of traditional aptitude, considering the discretization methods, the controller structures and the kinds of plants (including - benchmarch - problems), under given specifications according to permanent and transitory systems.
Esta disertación presenta una comparación entre técnicas de discretización de controladores, considerando diferentes extructuras de control. Los tipos de sistemas estudiados en este trabajo de investigación son sistemas lineales, invariantes en el tiempo, determinísticos, causales y univariados. Se compara el desempeño de las técnicas de discretización utilizando figuras de mérito tradicionales, considerando los métodos de discretización, las extructuras de los controladores y los tipos de planta habituales (incluyendo problemas - benchmarch - ), bajo especificaciones dadasen relación a los régimenes permanente y transiente.

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Botti, Michele. "Advanced polyhedral discretization methods for poromechanical modelling." Thesis, Montpellier, 2018. http://www.theses.fr/2018MONTS041/document.

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Dans cette thèse, on s’intéresse à de nouveaux schémas de discrétisation afin de résoudre les équations couplées de la poroélasticité et nous présentons des résultats analytiques et numériques concernant des problèmes issus de la poromécanique. Nous proposons de résoudre ces problèmes en utilisant les méthodes Hybrid High-Order (HHO), une nouvelle classe de méthodes de discrétisation polyédriques d’ordre arbitraire. Cette thèse a été conjointement financée par le Bureau de Recherches Géologiques et Minières (BRGM) et le LabEx NUMEV. Le couplage entre l’écoulement souterrain et la déformation géomécanique est un sujet de recherche crucial pour les deux institutions de cofinancement
In this manuscript we focus on novel discretization schemes for solving the coupled equations of poroelasticity and we present analytical and numerical results for poromechanics problems relevant to geoscience applications. We propose to solve these problems using Hybrid High-Order (HHO) methods, a new class of nonconforming high-order methods supporting general polyhedral meshes. This Ph.D. thesis was conjointly founded by the Bureau de recherches géologiques et minières (BRGM) and LabEx NUMEV. The coupling between subsurface flow and geomechanical deformation is a crucial research topic for both cofunding institutions

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Willquist, André. "Uncertainty Discretization for Motion Planning Under Uncertainty." Thesis, Linköpings universitet, Institutionen för datavetenskap, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-170496.

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In this thesis, the problem of motion planning under uncertainty is explored. Motion planning under uncertainty is important since even with noise during the execution of the plan, it is desirable to keep the collision risk low. However, for the motion planning to be useful it needs to be possible to perform it in a reasonable time. The introduction of state uncertainty leads to a substantial increase in search time due to the additional dimensions it adds to the search space. In order to alleviate this problem, different approaches to pruning of the search space are explored. The initial approach is to prune states based on having strictly worse uncertainty and path cost than other found states. Having performed this initial pruning, an alternate approach to comparing uncertainties is examined in order to explore if it is possible to achieve a lower search time. The approach taken in order to lower the search time further is to discretize the covariance of a state by using a number of buckets. However, this discretization results in giving up the completeness and optimality of the algorithm. Having implemented these different ways of pruning, their performance is tested on a number of different scenarios. This is done by evaluating the planner using the pruning in several different scenarios including uncertainty and one without uncertainty. It is found that all of the pruning approaches reduce the overall search time compared to when no additional pruning based on the uncertainty is done. Additionally, it is indicated that the bucket-based approach reduce the search time to a greater extent than the strict pruning approach. Furthermore, the extensions made results in no increase in cost or a very small increase in cost for the explored scenarios. Based on these results, it is likely that the bucket pruning approach has some potential. However more studies, particularly with additional scenarios, needs to be made before any definitive conclusions can be made.

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Bürgler, Josef Franz. "Discretization and grid adaptation in semiconductor device modeling /." [S.l.] : [s.n.], 1990. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=9146.

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De, Rango Stan. "Higher-order spatial discretization for turbulent aerodynamic flows." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63580.pdf.

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15

Windholz, Thomas. "Strategies for Handling Spatial Uncertainty due to Discretization." Fogler Library, University of Maine, 2001. http://www.library.umaine.edu/theses/pdf/Windholz.pdf.

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16

Nguyen, Thu Huong. "Strong Stability Preserving Hermite-Birkhoff Time Discretization Methods." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23491.

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The main goal of the thesis is to construct explicit, s-stage, strong-stability-preserving (SSP) Hermite–Birkhoff (HB) time discretization methods of order p with nonnegative coefficients for the integration of hyperbolic conservation laws. The Shu–Osher form and the canonical Shu–Osher form by means of the vector formulation for SSP Runge–Kutta (RK) methods are extended to SSP HB methods. The SSP coefficients of k-step, s-stage methods of order p, HB(k,s,p), as combinations of k-step methods of order (p − 3) with s-stage explicit RK methods of order 4, and k-step methods of order (p-4) with s-stage explicit RK methods of order 5, respectively, for s = 4, 5,..., 10 and p = 4, 5,..., 12, are constructed and compared with other methods. The good efficiency gains of the new, optimal, SSP HB methods over other SSP methods, such as Huang’s hybrid methods and RK methods, are numerically shown by means of their effective SSP coefficients and largest effective CFL numbers. The formulae of these new, optimal methods are presented in their Shu–Osher form.

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Alimin, E. K. "Dissipation and discretization in time marching CFD calculation." Thesis, Cranfield University, 1995. http://hdl.handle.net/1826/4021.

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This thesis concentrates on accuracy improvements for an existing software package that solves the three dimensional Reynolds Averaged Navier-Stokes equations in rotating coordinates. It is a cell centred explicit time marching code. Two topics are considered: improvement to the discretization scheme, and reduction of the artificial dissipation. The first topic is the analysis of the straight averaging process which demonstrates that the process can result in inconsistency with a skewed grid. An alternative consistent scheme is proposed which is based upon quadratic interpolation. Improved accuracy can also be obtained by modifying the grid or adopting a cell vertex scheme. The stability of the iterative process is also shown to depend on the time step. The reduction of artificial dissipation (second topic) first considers the role of the so called aspectratio and velocity functions. These are found to be limited in influence and a new function is proposed based upon the local flow gradient. Both two and three dimensional turbomachinery cases are tested and improvements demonstrated. In the second part of the analysis, the eigenvalues of the stability matrix are used to reduce the dissipation in overdamped regions. Again this method is applied to various test cases and improvements demonstrated. The management part of this Total Technology PhD Program discusses topics concerned with collaboration and technology development in the aero engine industry with particular emphasis on the role of an "emerging" partner.

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Angoshtari, Arzhang. "Geometric discretization schemes and differential complexes for elasticity." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/49026.

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In this research, we study two different geometric approaches, namely, the discrete exterior calculus and differential complexes, for developing numerical schemes for linear and nonlinear elasticity. Using some ideas from discrete exterior calculus (DEC), we present a geometric discretization scheme for incompressible linearized elasticity. After characterizing the configuration manifold of volume- preserving discrete deformations, we use Hamilton’s principle on this configuration manifold. The discrete Euler-Lagrange equations are obtained without using Lagrange multipliers. The main difference between our approach and the mixed finite element formulations is that we simultaneously use three different discrete spaces for the displacement field. We test the efficiency and robustness of this geometric scheme using some numerical examples. In particular, we do not see any volume locking and/or checkerboarding of pressure in our numerical examples. This suggests that our choice of discrete solution spaces is compatible. On the other hand, it has been observed that the linear elastostatics complex can be used to find very efficient numerical schemes. We use some geometric techniques to obtain differential complexes for nonlinear elastostatics. In particular, by introducing stress functions for the Cauchy and the second Piola-Kirchhoff stress tensors, we show that 2D and 3D nonlinear elastostatics admit separate kinematic and kinetic complexes. We show that stress functions corresponding to the first Piola-Kirchhoff stress tensor allow us to write a complex for 3D nonlinear elastostatics that similar to the complex of 3D linear elastostatics contains both the kinematics an kinetics of motion. We study linear and nonlinear compatibility equations for curved ambient spaces and motions of surfaces in R3. We also study the relationship between the linear elastostatics complex and the de Rham complex. The geometric approach presented in this research is crucial for understanding connections between linear and nonlinear elastostatics and the Hodge Laplacian, which can enable one to convert numerical schemes of the Hodge Laplacian to those for linear and possibly nonlinear elastostatics.

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RAMOS, MARCIA DA ROCHA. "A STUDY OF DISCRETIZATION METHODS TO CONTROL ENGINEERING." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1997. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8783@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Este trabalho apresenta um estudo sobre métodos de discretização aplicados à engenharia de Controle. É feita uma revisão dos sistemas lineares de controle discreto, ressaltando suas principais propriedades, assim como suas respostas no tempo e na freqüência. Também são apresentadas as figuras de mérito, que servirão como base de comparação de desempenho dos sistemas, e os tipos de conversores de sinais utilizados. O experimento é então apresentado e são discutidos todos os procedimentos para a sua realização através de um exemplo. Os controladores utilizados são apresentados e suas funções de transferências são fornecidas para sua posterior discretização. Finalmente são listados os resultados obtidos nas simulações utilizando tabelas e gráficos comparativos.
This work presents a study of some discretization methods applied to Control Engineering. A review of discrete control linear systems, their properties and reponses in the and frequency domains are presented, as well as the figures, used to compare their performances, and the signal conversors used in this work. The experiment, the procedures, the controllers and their transfer functions are shown and the simulations results are presented in tables and graphics.

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Schraeder, Daniela. "Analytically divergence-free discretization methods for Darcy's problem." Thesis, University of Sussex, 2010. http://sro.sussex.ac.uk/id/eprint/2327/.

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Radial basis functions are well known for their applications in scattered data approximation and interpolation. They can also be applied in collocation methods to solve partial differential equations. We develop and analyse a mesh-free discretization method for Darcy's problem. Our approximation scheme is based upon optimal recovery, which leads to a collocation scheme using divergence-free positive denite kernels. Besides producing analytically incompressible flow fields, our method can be of arbitrary order, works in arbitrary space dimension and for arbitrary geometries. Firstly we establish Darcy's problem. To introduce the scheme we review and study divergence-free and curl-free matrix-valued kernels and their reproducing kernel Hilbert spaces. After developing the scheme, we find the approximation error for smooth target functions and the optimal approximation orders. Furthermore, we develop Sobolev-type error estimates for target functions rougher than the approximating function and show that the approximation properties extend to those functions. To find these error estimates, we apply band-limited approximation. Finally, we illustrate the method with numerical examples.

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McGrory, William Dandridge. "Generalized spatial discretization techniques for space-marching algorithms." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/37228.

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Gautham, Tejaswini. "Residual-Based Discretization Error Estimation for Unsteady Flows." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/96400.

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Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is important to have rigorous techniques to estimate the error produced when using CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is extended for the unsteady case. Numerical results are presented for the steady viscous Burgers' equation, unsteady viscous Burgers' equation, steady quasi-1D Euler equations, and unsteady 1D Euler equations when applied to a shock tube. Cases using either defect correction or ETE are shown to give higher orders of accuracy for the corrected discretization error estimates when compared to the discretization error of the primal solution.
Master of Science
Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is used to understand complex flows that are difficult to replicate using experimental techniques or by theoretical methods. It is important to have rigorous techniques to estimate the error produced when using CFD even when the exact solution is not available for comparison. This paper develops techniques to estimate discretization error for unsteady flows. Discretization error has one of the largest error magnitudes in CFD solutions. The exact physics dictates the use of continuous equations but to apply CFD techniques, the continuous equations have to be converted to discrete equations. Truncation error is, the error obtained when converting the continuous equations to discrete equations. This truncation error is in turn, the local source term for discretization error. To reduce the discretization error in the discrete equations, the exact or estimated truncation error is either added as a source term to the discrete equations or is used along with the error transport equation to get a better estimate of the solutions. A framework to obtain exact truncation error and estimated truncation error is also presented. The framework is first applied to the steady equations and is verified with results from previous studies and is then extended to the unsteady flows.

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Hüeber, Stefan. "Discretization techniques and efficient algorithms for contact problems." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-36087.

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Stern, Ari Marsden Jerrold E. Marsden Jerrold E. Desbrun Mathieu. "Geometric discretization of Lagrangian mechanics and field theories /." Diss., Pasadena, Calif. : Caltech, 2009. http://resolver.caltech.edu/CaltechETD:etd-12312008-173851.

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Seufer, Ingo. "Generalized inverses of differential-algebraic equations and their discretization." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980230306.

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Kaphle, Manindra. "Simulations of human movements through temporal discretization and optimization." Licentiate thesis, KTH, Mechanics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4585.

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Study of physical phenomena by means of mathematical models is common in various branches of engineering and science. In biomechanics, modelling often involves studying human motion by treating the body as a mechanical system made of interconnected rigid links. Robotics deals with similar cases as robots are often designed to imitate human behavior. Modelling human movements is a complicated task and, therefore, requires several simplifications and assumptions. Available computational resources often dictate the nature and the complexity of the models. In spite of all these factors, several meaningful results are still obtained from the simulations.

One common problem form encountered in real life is the movement between known initial and final states in a pre-specified time. This presents a problem of dynamic redundancy as several different trajectories are possible to achieve the target state. Movements are mathematically described by differential equations. So modelling a movement involves solving these differential equations, along with optimization to find a cost effective trajectory and forces or moments required for this purpose.

In this study, an algorithm developed in Matlab is used to study dynamics of several common human movements. The main underlying idea is based upon temporal finite element discretization, together with optimization. The algorithm can deal with mechanical formulations of varying degrees of complexity and allows precise definitions of initial and target states and constraints. Optimization is carried out using different cost functions related to both kinematic and kinetic variables.

Simulations show that generally different optimization criteria give different results. To arrive on a definite conclusion on which criterion is superior over others it is necessary to include more detailed features in the models and incorporate more advanced anatomical and physiological knowledge. Nevertheless, the algorithm and the simplified models present a platform that can be built upon to study more complex and reliable models.

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Rücker, Carsten. "Advanced Electrical Resistivity Modelling and Inversion using Unstructured Discretization." Doctoral thesis, Universitätsbibliothek Leipzig, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-69066.

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In this dissertation an approach is presented for the three-dimensional electrical resistivity tomography (ERT) using unstructured discretizations. The geoelectrical forward problem is solved by the finite element method using tetrahedral meshes with linear and quadratic shape functions. Unstructured meshes are suitable for modelling domains of arbitrary geometry (e.g., complicated topography). Furthermore, the best trade-off between accuracy and numerical effort can be achieved due to the capability of problem-adapted mesh refinement. Unstructured discretizations also allow the consideration of spatial extended finite electrodes. Due to a corresponding extension of the forward operator using the complete electrode model, known from medical impedance tomography, a study about the influence of such electrodes to geoelectrical measurements is given. Based on the forward operator, the so-called triple-grid-technique is developed to solve the geoelectrical inverse problem. Due to unstructured discretization, the ERT can be applied by using a resolution dependent parametrization on arbitrarily shaped two-dimensional and three-dimensional domains. A~Gauss-Newton method is used with inexact line search to fit the data within error bounds. A global regularization scheme is applied using special smoothness constraints. Furthermore, an advanced regularization scheme for the ERT is presented based on unstructured meshes, which is able to include a-priori information into the inversion and significantly improves the resulting ERT images. Structural information such as material interfaces known from other geophysical techniques are incorporated as allowed sharp resistivity contrasts. Model weighting functions can define individually the allowed deviation of the final resistivity model from given start or reference values. As a consequent further development the region concept is presented where the parameter domain is subdivided into lithological or geological regions with individual inversion and regularization parameters. All used techniques and concepts are part of the open source C++ library GIMLi, which has been developed during this thesis as an advanced tool for the method-independent solution of the inverse problem.

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Sermeus, Kurt. "Multi-dimensional upwind discretization and application to compressible flows." Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209519.

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This thesis is concerned with the further development and analysis of a class of Computational Fluid Dynamics (CFD) methods for the numerical simulation of compressible flows on unstructured grids, known as Residual Distribution (RD).

The RD method constitutes a class of discretization schemes for hyperbolic systems

of conservation laws, which forms an attractive alternative to the more classical Finite Volume methods, particularly since it allows better representation of the flow physics by genuinely multi-dimensional upwinding and offers second-order accuracy on a compact stencil.

Despite clear advantages of RD schemes, they also have some unexpected anomalies in common with Finite Volume methods and an attempt to resolve them is presented. The most notable anomaly is the violation of the entropy condition, which as a consequence allows unphysical expansion shocks to exist in the numerical solution. In the thesis the genuinely multi-dimensional character of this anomaly is analyzed and a multi-dimensional entropy fix is presented and shown to avoid expansion shocks. Another infamous anomaly is the carbuncle phenomenon, an instability observed in many numerical solutions with strong shocks, such as the bow shock on a blunt body in hypersonic flow. The occurence of the carbuncle phenomenon with RD methods is analyzed and a novel formulation for a shock fix, based on an anisotropic diffusion term added in the shock layer, is presented and shown to cure the anomaly in 2D and 3D hypersonic flow problems.

In the present work an effort has been made also to an objective and quantitative assessment of the merits of the RD method for typical aerodynamical engineering applications, such as the transonic flow over airfoils and wings.

Validation examples including inviscid, laminar as well as high Reynolds number turbulent flows

and comparisons against results from state-of-the-art Finite Volume methods are presented.

It is shown that the second-order multi-dimensional upwind RD schemes have an accuracy which is at least as good as second-order FV methods using dimension-by-dimension upwinding and that their main advantage lies in providing excellent monotone shock capturing.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

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Rafee, Nadra. "Optimal multirate discretization of analog controllers, theory and application." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq20765.pdf.

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Giannacopoulos, Dennis. "Optimal discretization-based adaptive finite element analysis for electromagnetics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0025/NQ50170.pdf.

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Jalali, Alireza. "Truncation error analysis of unstructured finite volume discretization schemes." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42429.

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Numerical experiments have proved that numerical errors are at least as large as other sources of error in numerical simulation of fluid flows. Approximating the continuous partial differential equations that govern the behavior of a fluid with discrete relations results in truncation error which is the initial source of numerical errors. Reducing numerical error requires the ability to quantify and reduce the truncation error. Although the truncation error can be easily found for structured mesh discretizations, there is no generic methodology for the truncation error analysis of unstructured finite volume discretizations. In this research, we present novel techniques for the analysis and quantification of the truncation error produced by finite volume discretization on unstructured meshes. These techniques are applied to compare the truncation error produced by different discretization schemes commonly used in cell-centered finite volume solvers. This comparison is carried out for fundamental scalar equations that model the fluid dynamic equations. These equations model both the diffusive and convective fluxes which appear in the finite volume formulation of the fluid flow equations. Two classes of tests are considered for accuracy assessment. Analytical tests on topologically perfect meshes are done to find the general form of the truncation error. Moreover, these tests allow us to eliminate from consideration those schemes that do not perform well even for slightly perturbed meshes. Given the results of the analytic tests, we define a truncation error metric based on the coefficients associated with the spatial derivatives in the series expansion of the truncation error. More complex numerical tests are conducted on the remaining schemes to extend the accuracy assessment to general unstructured meshes consisting of both isotropic and anisotropic triangles. These results will guide us in the choice of appropriate discretization schemes for diffusive and convective fluxes arising from discretization of real governing equations.

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Giannacopoulos, Dennis. "Optimal discretization-based adaptive finite element analysis for electromagnetics." Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=35885.

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One of the primary objectives of adaptive finite element analysis research is to determine how to effectively discretize a problem in order to obtain a sufficiently accurate solution efficiently. Consequently, a major research issue in adaptive finite element analysis is the feedback control system used to guide the adaption; essentially, one needs to resolve which error data to feed back after each iteration, and how to use it to initialize the next adaptive step. Currently, there exists substantial evidence suggesting that the optimality of a finite element discretization plays a significant role in the accuracy of computed solutions at given levels of problem refinement. Therefore, in order to exploit the potential benefits in adaptive finite element methods, the characterization of optimal finite element discretizations has been investigated extensively. However, valid criteria for characterizing optimal finite element discretizations for a sufficiently wide range of problem applications have not been reported. A theoretical formulation for the numerical study of optimal finite element solutions to partial differential equations of macroscopic electromagnetics is presented. The formulation is based on variational aspects of optimal discretizations for Helmholtz systems that are closely related to the underlying stationarity principle used in computing finite element solutions to continuum problems. The optimal characteristics of approximate finite element solutions, as predicted by the theory and observed numerically, have been employed to develop new optimal discretization-based feedback refinement criteria for use with advanced strategy adaption models in finite element electromagnetics. Numerical tests indicate that they are effective and economical for efficiently and reliably guiding practical h-, p- and hp-type adaption models towards accurate solutions.
In addition, a series of important benchmark adaption problems are introduced to examine the validity of the theoretical concepts and the practical value of the new refinement criteria. Moreover, many of the computational and theoretical difficulties inherent in the currently available characterizations of optimal finite element discretizations are explained and illustrated with numerical results computed for the same benchmark problems.

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Phillips, Tyrone. "Residual-based Discretization Error Estimation for Computational Fluid Dynamics." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/50647.

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The largest and most difficult numerical approximation error to estimate is discretization error. Residual-based discretization error estimation methods are a category of error estimators that use an estimate of the source of discretization error and information about the specific application to estimate the discretization error using only one grid level. The higher-order terms are truncated from the discretized equations and are the local source of discretization error. The accuracy of the resulting discretization error estimate depends solely on the accuracy of the estimated truncation error. Residual-based methods require only one grid level compared to the more commonly used Richardson extrapolation which requires at least two. Reducing the required number of grid levels reduces computational expense and, since only one grid level is required, can be applied to unstructured grids where multiple quality grid levels are difficult to produce. The two residual-based discretization error estimators of interest are defect correction and error transport equations. The focus of this work is the development, improvement, and evaluation of various truncation error estimation methods considering the accuracy of the truncation error estimate and the resulting discretization error estimates. The minimum requirements for accurate truncation error estimation is specified along with proper treatment for several boundary conditions. The methods are evaluated using various Euler and Navier-Stokes applications. The discretization error estimates are compared to Richardson extrapolation. The most accurate truncation error estimation method was found to be the k-exact method where the fine grid with a correction factor was considerably reliable. The single grid methods including the k-exact require that the continuous operator be modified at the boundary to be consistent with the implemented boundary conditions. Defect correction showed to be more accurate for areas of larger discretization error; however, the cost was substantial (although cheaper than the primal problem) compared to the cost of solving the ETEs which was essential free due to the linearization. Both methods showed significantly more accurate estimates compared to Richardson extrapolation especially for smooth problems. Reduced accuracy was apparent with the presence of stronger shocks and some possible modifications to adapt to singularies are proposed for future work.
Ph. D.

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Matringe, Sébastien François. "Mixed finite element methods for discretization and streamline tracing /." May be available electronically:, 2008. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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Zhu, Lei. "A discontinuous least-squares spatial discretization for the sn equations." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-3026.

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Rasch, Christian Mark Anton. "Numerical discretization of static Hamilton-Jacobi equations on triangular meshes." [S.l.] : [s.n.], 2007. http://mediatum2.ub.tum.de/doc/604594/document.pdf.

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Bailey, Teresa S. "A piecewise linear finite element discretization of the diffusion equation." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4331.

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In this thesis, we discuss the development, implementation and testing of a piecewise linear (PWL) continuous Galerkin finite element method applied to the threedimensional diffusion equation. This discretization is particularly interesting because it discretizes the diffusion equation on an arbitrary polyhedral mesh. We implemented our method in the KULL software package being developed at Lawrence Livermore National Laboratory. This code previously utilized Palmer's method as its diffusion solver, which is a finite volume method that can produce an asymmetric coefficient matrix. We show that the PWL method produces a symmetric positive definite coefficient matrix that can be solved more efficiently, while retaining the accuracy and robustness of Palmer's method. Furthermore, we show that in most cases Palmer's method is actually a non-Galerkin PWL finite element method. Because the PWL method is a Galerkin finite element method, it has a firm theoretical background to draw from. We have shown that the PWL method is a well-posed discrete problem with a second-order convergence rate. We have also performed a simple mode analysis on the PWL method and Palmer's method to compare the accuracy of each method for a certain class of problems. Finally, we have run a series of numerical tests to uncover more properties of both the PWL method and Palmer's method. These numerical results indicate that the PWL method, partially due to its symmetric matrix, is able to solve large-scale diffusion problems very efficiently.

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Weller, Stephan [Verfasser], and Eberhard [Akademischer Betreuer] Bänsch. "Time discretization for capillary problems / Stephan Weller. Gutachter: Eberhard Bänsch." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2015. http://d-nb.info/107709941X/34.

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Hardering, Hanne [Verfasser]. "Intrinsic Discretization Error Bounds for Geodesic Finite Elements / Hanne Hardering." Berlin : Freie Universität Berlin, 2015. http://d-nb.info/1074871022/34.

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Tahiri, Ahmed. "A compact discretization method for diffusion problems with local refinement." Doctoral thesis, Universite Libre de Bruxelles, 2002. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211417.

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Tam, Anita W. "High-order spatial discretization methods for the shallow water equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58942.pdf.

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Nguyen, Hanh. "Grid discretization effects in the presence of realistic geological heterogeneities." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ60481.pdf.

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Raalte, Marc Hartog van. "Multigrid analysis and embedded boundary conditions for discontinuous Galerkin discretization." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2004. http://dare.uva.nl/document/75029.

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Tuncer, Necibe Meir Amnon J. "A novel finite element discretization of domains with spheroidal geometry." Auburn, Ala., 2007. http://repo.lib.auburn.edu/Send%2011-10-07/TUNCER_NECIBE_24.pdf.

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Kuo, Chung-Chieh. "Discretization and solution of elliptic PDEs--a transform domain approach." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/14656.

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Schlegel, Martin. "Adaptive discretization methods for the efficient solution of dynamic optimization problems /." Düsseldorf : VDI-Verl, 2005. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=013053068&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Constantiniu, Alexandru [Verfasser]. "A hybrid nodal-element-based discretization method / vorgelegt von Alexandru Constantiniu." Erlangen : Lehrstuhl für Techn. Mechanik, Univ. Erlangen-Nürnberg, 2010. http://d-nb.info/1009552325/34.

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Hampus, Forsberg. "Automatic lumped element discretization of curved beams with variable sectional area." Thesis, Umeå universitet, Institutionen för fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-145058.

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Calculations on stress, strain and deformation are typically made using finite element methods (FEM). An alternative to this is a rigid bodydynamics approach also called lumped element method (LEM). LEM implements deformation by replacing single rigid bodies with multiple subbodies, which are in turn connected with joints (also called constraints) that allow movement between the sub-bodies. If instead of FEM, a lumped element method is used to simulate deformable objects, sufficient accuracy can be obtained at a much lower cost, complexity-wise. A lumped element method-approach could for example achieve real-time simulationspeed. The purpose of this thesis is to expand upon previous work into LEM, analyzing how the rigid bodies and constraints should be configured to produce accurate results for a wider range of objects. Specifically, beams of varying cross section and curved beam axis, as well as other test cases. The simulated values are compared with the analytic predictions given by Euler-Bernoulli beam theory. These simulations are implemented using the AGX Dynamics physics engine from Algoryx Simulation AB. One intended application area of LEM is crane arms. This motivates the focus on analyzing how LEM behaves when simulating beams, as they represent the most basic version of crane arms. Simulation and testing of full crane objects was unfortunately not accomplished, partly due to a lack of convenient testing data. Further work is needed to confirm that LEM behaves well for these expanded cases as well. In addition to the analysis section above, the purpose is also to implement a pipeline for automatic conversion of a CAD-model to a lumped element version in AGX. Specifically, a CAD-model given in the 3D-modeling software SpaceClaim.

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Takagi, Kentaro, Ichiro Jikuya, Gou Nishida, Maschke Bernhard, and Kinji Asaka. "A study on the discretization of a distributed RC circuit model." IEEE, 2008. http://hdl.handle.net/2237/13888.

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Rückert, Jens. "Kirchhoff Plates and Large Deformations - Modelling and C^1-continuous Discretization." Doctoral thesis, Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-121275.

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In this thesis a theory for large deformation of plates is presented. Herein aspects of the common 3D-theory for large deformation with the Kirchhoff hypothesis for reducing the dimension from 3D to 2D is combined. Even though the Kirchhoff assumption was developed for small strain and linear material laws, the deformation of thin plates made of isotropic non-linear material was investigated in a numerical experiment. Finally a heavily deformed shell without any change in thickness arises. This way of modeling leads to a two-dimensional strain tensor essentially depending on the first two fundamental forms of the deformed mid surface. Minimizing the resulting deformation energy one ends up with a nonlinear equation system defining the unknown displacement vector U. The aim of this thesis was to apply the incremental Newton technique with a conformal, C^1-continuous finite element discretization. For this the computation of the second derivative of the energy functional is the key difficulty and the most time consuming part of the algorithm. The practicability and fast convergence are demonstrated by different numerical experiments.

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Dissertations / Theses on the topic 'Discretization'

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