Dissertations / Theses on the topic 'Discontinuous Function'
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Costin, William James. "Radial basis function interpolation applied to discontinuous mesh interfaces." Thesis, University of Bristol, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.653069.
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For large-scale Computational Fluid Dynamics (CFD) simulations it is often necessary to divide the domain into a mesh of discrete points or volumes. However, the domain can also be split into a set of zones separated by interfaces, allowing the zones to be meshed individually. Discontinuous or nonmatching mesh spacing across the zonal interfaces offers many advantages, particularly in terms of easing the mesh generation process, reduction of required mesh densities, and relative motion between mesh zones. However, accurate data transfer across the interfaces is required for global solution accuracy to be maintained. A more versatile data transfer method for discontinuous interfaces has the potential to reduce both the complexity of, and constraints place on, the process of discretising complex domains. This research was motivated by work on large-scale parallelised CFD simulations using high quality structured multiblock meshes. For such tasks the accuracy of the final result has a significant dependence on the quality of the mesh used to discretise the domain. The mesh is split into separate zones for parallel computation but must be generated as a topographically consistent whole, rather than individually for each zone. The objective therefore was to create a new method of discontinuous interface data transfer that does not place topographic limitations on the mesh, simplifying the mesh generation process. To this end, the fields of flow solution, high accuracy interpolation and mesh generation have been investigated with the aim of formulating and assessing a new data transfer approach. A new data transfer method based on Radial Basis Function (RBF) interpolation is developed and presented. Strategies for the construction of the interpolation data set are compared and a new more advanced approach developed. A series of analytical tests are used to assess the properties of the new method: Both the order of accuracy of the method and the ability to accurately model the full range of frequency content are considered. The method is applied to both finite difference and finite volume numerical solutions. For the latter both multi-grid discretisation and parallelised solution have been ,j ABSTRACT implemented as part of integration into an existing parallel, multiblock, multi grid compressible flow solver. Additionally, the relative merits and cost of localised and global forms of the method are assessed. The method has been applied to a series of aeronautical test cases including a subsonic and transonic aerofoil. The results show that the method is both effective and robust, providing accurate transmission for well and poorly conceived interface geometries. One great success is that in generic form the method remains applicable to all iterative solution methods with similar domain discretisation requirements; as a result there are many opportunities for further work.
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Dubois, Olivier 1980. "Optimized Schwarz methods for the advection-diffusion equation and for problems with discontinuous coefficients." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103379.
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Optimized Schwarz methods are iterative domain decomposition procedures with greatly improved convergence properties, for solving second order elliptic boundary value problems. The enhanced convergence is obtained by replacing the Dirichlet transmission conditions in the classical Schwarz iteration with more general conditions that are optimized for performance. The convergence is optimized through the solution of a min-max problem. The theoretical study of the min-max problems gives explicit formulas or characterizations for the optimized transmission conditions for practical use, and it permits the analysis of the asymptotic behavior of the convergence.In the first part of this work, we continue the study of optimized transmission conditions for advection-diffusion problems with smooth coefficients. We derive asymptotic formulas for the optimized parameters for small mesh sizes, in the overlapping and non-overlapping cases, and show that these formulas are accurate when the component of the advection tangential to the interface is not too large.
In a second part, we consider a diffusion problem with a discontinuous coefficient and non-overlapping domain decompositions. We derive several choices of optimized transmission conditions by thoroughly solving the associated min-max problems. We show in particular that the convergence of optimized Schwarz methods improves as the jump in the coefficient increases, if an appropriate scaling of the transmission conditions is used. Moreover, we prove that optimized two-sided Robin conditions lead to mesh-independent convergence. Numerical experiments with two subdomains are presented to verify the analysis. We also report the results of experiments using the decomposition of a rectangle into many vertical strips; some additional analysis is carried out to improve the optimized transmission conditions in that case.
On a third topic, we experiment with different coarse space corrections for the Schwarz method in a simple one-dimensional setting, for both overlapping and non-overlapping subdomains. The goal is to obtain a convergence that does not deteriorate as we increase the number of subdomains. We design a coarse space correction for the Schwarz method with Robin transmission conditions by considering an augmented linear system, which avoids merging the local approximations in overlapping regions. With numerical experiments, we demonstrate that the best Robin conditions are very different for the Schwarz iteration with, and without coarse correction.
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COLOMBO, Alessandro (ORCID:0000-0002-6527-8148). "An agglomeration-based discontinuous Galerkin method for compressible flows." Doctoral thesis, Università degli studi di Bergamo, 2011. http://hdl.handle.net/10446/222124.
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This thesis investigates the flexibility associated to Discontinuous Galerkin (DG) discretization on very general meshes obtained by means of agglomeration techniques. The work begins with a brief overview of the main tools that have been extended or specifically developed to deal with arbitrarily shaped elements in the DG context. Then two different implementations of the BRMPS scheme introduced by Bassi, Rebay, Mariotti, Pedinotti and Savini in [16] for the DG discretization of the Laplace operator on arbitrarily shaped elements have been presented. The validation of the scheme on a Poisson problem shows that the discrete polynomial space preserves optimal convergence properties. The discretization of the second order differential operator has been directly extended to the Navier-Stokes equations and the Reynolds Averaged Navier-Stokes (RANS) equations coupled with the k-w turbulence model of Wilcox [54]. In this regard, an implicit time integration strategy has been considered and assessed on classical validation test cases for the compressible f uid dynamics. Then a simple alternative approach to high-order mesh generation is presented. Indeed, once a standard fine grid able to provide an accurate domain discretization has been produced by means of standard low-order grid generation tools, a computational mesh suitable for the desired accuracy and computationally affordable can be obtained via agglomeration while keeping the boundary resolution of the fine grid. The effectiveness of this approach in representing the geometry of the domain is numerically assessed both on a Poisson model problem and on challenging inviscid and viscous test cases. Finally, the freedom in simply defining the topology of agglomerated meshes leads to a nonstandard approach to h-adaptivity that exploits adaptive agglomeration coarsening of a properly fine underlying grid. The effectiveness of this approach has been assessed on test cases involving both error-based and fl ow feature-based simple estimators.
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Li, Tianyu. "On the Formulation of a Hybrid Discontinuous Galerkin Finite Element Method (DG-FEM) for Multi-layered Shell Structures." Thesis, Virginia Tech, 2016. http://hdl.handle.net/10919/82962.
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A high-order hybrid discontinuous Galerkin finite element method (DG-FEM) is developed for multi-layered curved panels having large deformation and finite strain. The kinematics of the multi-layered shells is presented at first. The Jacobian matrix and its determinant are also calculated. The weak form of the DG-FEM is next presented. In this case, the discontinuous basis functions can be employed for the displacement basis functions. The implementation details of the nonlinear FEM are next presented. Then, the Consistent Orthogonal Basis Function Space is developed. Given the boundary conditions and structure configurations, there will be a unique basis function space, such that the mass matrix is an accurate diagonal matrix. Moreover, the Consistent Orthogonal Basis Functions are very similar to mode shape functions. Based on the DG-FEM, three dedicated finite elements are developed for the multi-layered pipes, curved stiffeners and multi-layered stiffened hydrofoils. The kinematics of these three structures are presented. The smooth configuration is also obtained, which is very important for the buckling analysis with large deformation and finite strain. Finally, five problems are solved, including sandwich plates, 2-D multi-layered pipes, 3-D multi-layered pipes, stiffened plates and stiffened multi-layered hydrofoils. Material and geometric nonlinearities are both considered. The results are verified by other papers' results or ANSYS.Master of Science
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Mello, João Paulo Ferreira de. "Funções de Melnikov para classes de sistemas descontínuos no plano." reponame:Repositório Institucional da UFABC, 2015.
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Orientador: Prof. Dr. Maurício Firmino Silva LimaDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2015.
Neste trabalho estudamos generalizações do Método de Melnikov para sistemas descontínuos no plano. Neste sentido, inicialmente abordamos esse problema como uma variação do estudo [1] onde um campo Hamiltoniano que admite um ciclo heteroclínico, cujo interior é folheado de órbitas periódicas, é perturbado por um campo Hamiltoniano não autonomo. Neste trabalho estendemos esse resultado para perturbações mais gerais (não conservativas) e apresentamos funções de Melnikov nesse novo contexto. Finalmente, abordamos o problema mais geral, relativo à perturbação de campos não conservativos, onde a função de Melnikov, associada a órbita heteroclínica, é obtida.
In this work we study generalizations of Melnikov's method to planar discontinuous dynamical system. Initially we study this problem as a variation of the work [1] where a Hamiltonian vector field that admits an heteroclinic cycle with its interior foliated by a family of periodic orbits is perturbed by a Hamiltonian perturbation. In this work we extended the results to more general perturbation (non conservative) and we show the Melnikov's functions in this new context. Finally, we approach a more general problem related to a perturbation of the non-conservative vector field where we obtained the Melnikov's function that is associated with a heteroclínic orbit.
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Santos, Iguer Luis Domini dos [UNESP]. "Análise de estabilidade de sistemas dinâmicos descontínuos e aplicações." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/94290.
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Neste trabalho introduzimos uma classe de sistemas dinâmicos descontínuos com espaço tempo contínuo e analisamos Teoremas que asseguram condições suficientes para a estabilidade de Lyapunov utilizando funções de Lyapunov. Além disso, consideramos também Teoremas de Recíproca, que sob algumas condições garantem uma determinada necessidade para esses Teoremas de estabilidade de Lyapunov.
In this work we introduce a class of discontinuous dynamical systems with time space continuous and we analyze Theorems that ensure sufficient conditions for the Lyapunov stability using Lyapunov functions. Moreover, we also consider Converse Theorems, which under some conditions guarantee a determined necessity for those Theorems of Lyapunov stability.
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Denniston, Jeffrey T. "A Study of Subsystems of Topological Systems Motivated by the Question of Discontinuity in TopSys." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1497095905660085.
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Wei, Jiangong. "Surface Integral Equation Methods for Multi-Scale and Wideband Problems." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408653442.
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He, Taiping. "Reaction-Diffusion Systems with Discontinuous Reaction Functions." NCSU, 2005. http://www.lib.ncsu.edu/theses/available/etd-03192005-101102/.
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This dissertation studies coupled reaction diffusion systems with discontinuous reaction functions. It includes three parts: The first part is concerned with the existence of solutions for a coupled system of two parabolic equations and the second part is devoted to the monotone iterative methods for monotone and mixed quasimonotone functions. Various monotone iterative schemes are presented and each of these schemes leads to an existence-comparison theorem and the monotone convergence of the maximal and minimal sequences. In the third part, the monotone iterative schemes are applied to compute numerical solutions of the system. These numerical solutions are based on the finite element method which gives a finite approximation of the coupled system. Numerical results for some scalar parabolic bounday problems and a coupled system of parabolic equations are also given.
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Díaz, Lolimar, and Raúl Naulin. "A set of almost periodic discontinuous functions." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95357.
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Liu, Guangwu. "Pathwise sensitivity estimation for expectations of discontinuous functions /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?IELM%202009%20LIU.
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Turski, Jacek. "Calculus of variations for discontinous fields and its applications to selected topics in continuum mechanics." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=72804.
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Mukhamedov, Farukh. "High performance computing for the discontinuous Galerkin methods." Thesis, Brunel University, 2018. http://bura.brunel.ac.uk/handle/2438/16769.
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Discontinuous Galerkin methods form a class of numerical methods to find a solution of partial differential equations by combining features of finite element and finite volume methods. Methods are defined using a weak form of a particular model problem, allowing for discontinuities in the discrete trial and test spaces. Using a discontinuous discrete space mesh provides proper flexibility and a compact discretisation pattern, allowing a multidomain and multiphysics simulation. Discontinuous Galerkin methods with a higher approximation polynomial order, the socalled p-version, performs better in terms of convergence rate, compared with the low order h-version with smaller element sizes and bigger mesh. However, the condition number of the Galerkin system grows subsequently. This causes surge in the amount of required storage, computational complexity and in the time required for computation. We use the following three approaches to keep the advantages and eliminate the disadvantages. The first approach will be a specific choice of basis functions which we call C1 polynomials. These ensure that the majority of integrals over the edge of the mesh elements disappears. This reduces the total number of non-zero elements in the resulting system. This decreases the computational complexity without loss in precision. This approach does not affect the number of iterations required by chosen Conjugate Gradients method when compared to the other choice of basis functions. It actually decreases the total number of algebraic operations performed. The second approach is the introduction of suitable preconditioners. In our case, the Additive two-layer Schwarz method, developed in [4], for the iterative Conjugate Gradients method is considered. This directly affects the spectral condition number of the system matrix and decreases the number of iterations required for the computation. This approach, however, increases the total number of algebraic operations and might require more operational time. To tackle the rise in the number of algebraic operations, we introduced a modified Additive two-layer non-overlapping Schwarz method with a Multigrid process. This using a fixed low-order approximation polynomial degree on a coarse grid. We show that this approach is spectrally equivalent to the first preconditioner, and requires less time for computation. The third approach is a development of an efficient mathematical framework for distributed data structure. This allows a high performance, massively parallel, implementation of the discontinuous Galerkin method. We demonstrate that it is possible to exploit properties of the system matrix and C1 polynomials as basis functions to optimize the parallel structures. The previously mentioned parallel data structure allows us to parallelize at the same time both the matrix-vector multiplication routines for the Conjugate Gradients method, as well as the preconditioner routines on the solver level. This minimizes the transfer ratio amongst the distributed system. Finally, we combined all three approaches and created a framework, which allowed us to successfully implement all of the above.
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Gorodetsky, Alex Arkady. "A learning method for the approximation of discontinuous functions for stochastic simulations." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/76101.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 79-83).
Surrogate models for computational simulations are inexpensive input-output approximations that allow expensive analyses, such as the forward propagation of uncertainty and Bayesian statistical inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, however, most existing surrogate construction methodologies yield large errors and slow convergence rates. This thesis develops a new methodology for approximating simulation outputs that depend discontinuously on input parameters. Our approach focuses on piecewise smooth outputs and involves two stages: first, efficient detection and localization of discontinuities in high-dimensional parameter spaces using polynomial annihilation, support vector machine classification, and uncertainty sampling; second, approximation of the output on each region using Gaussian process regression. The discontinuity detection methodology is illustrated on examples of up to 11 dimensions, including algebraic models and ODE systems, demonstrating improved scaling and efficiency over other methods found in the literature. Finally, the complete surrogate construction approach is demonstrated on two physical models exhibiting canonical discontinuities: shock formation in Burgers' equation and autoignition in hydrogen-oxygen combustion.
by Alex Arkady Gorodetsky.
S.M.
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Shlapunov, Alexander, and Nikolai Tarkhanov. "On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5775/.
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We consider a Sturm-Liouville boundary value problem in a bounded domain D of
R^n. By this is meant that the differential equation is given by a second order
elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types.
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Gioev, Dimitri. "Generalizations of Szego Limit Theorem : Higher Order Terms and Discontinuous Symbols." Doctoral thesis, KTH, Mathematics, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3123.
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Santos, Iguer Luis Domini dos. "Análise de estabilidade de sistemas dinâmicos descontínuos e aplicações /." São José do Rio Preto : [s.n.], 2008. http://hdl.handle.net/11449/94290.
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Resumo: Neste trabalho introduzimos uma classe de sistemas dinâmicos descontínuos com espaço tempo contínuo e analisamos Teoremas que asseguram condições suficientes para a estabilidade de Lyapunov utilizando funções de Lyapunov. Além disso, consideramos também Teoremas de Recíproca, que sob algumas condições garantem uma determinada necessidade para esses Teoremas de estabilidade de Lyapunov.Abstract: In this work we introduce a class of discontinuous dynamical systems with time space continuous and we analyze Theorems that ensure sufficient conditions for the Lyapunov stability using Lyapunov functions. Moreover, we also consider Converse Theorems, which under some conditions guarantee a determined necessity for those Theorems of Lyapunov stability.
Orientador: Geraldo Nunes Silva
Coorientador: Luis Antônio Fernandes de Oliveira
Banca: Luis Antônio Barrera San Martin
Banca: Adalberto Spezamiglio
Mestre
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Маслов, Олександр Петрович, Александр Петрович Маслов, Oleksandr Petrovych Maslov, and М. К. Супруненко. "Чисельне дослідження наближення розривних функцій." Thesis, Сумський державний університет, 2017. http://essuir.sumdu.edu.ua/handle/123456789/65560.
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Chilton, Ryan Austin. "H-, P- and T-Refinement Strategies for the Finite-Difference-Time-Domain (FDTD) Method Developed via Finite-Element (FE) Principles." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1219064270.
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Bahroun, Sami. "Modélisation et approche thermodynamique pour la commande des réacteurs chimiques catalytiques triphasiques continus et discontinus." Phd thesis, Université Claude Bernard - Lyon I, 2010. http://tel.archives-ouvertes.fr/tel-00720906.
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L'objet de cette thèse est la modélisation et la commande par approche thermodynamique des réacteurs catalytiques triphasiques en mode continu et en mode discontinu. Ce type de réacteur consiste en un système fortement non linéaire, multivariable et siège de réactions exothermiques. Nous utilisons les concepts de la thermodynamique irréversible pour la synthèse de lois de commande stabilisante pour ces deux types de réacteurs chimiques. En effet, la stricte concavité de la fonction d'entropie nous a permis de définir une fonction de stockage qui sert de fonction de Lyapunov candidate : la disponibilité thermodynamique. Nous utilisons cette fonction de disponibilité thermodynamique pour la synthèse de lois de commande stabilisante d'un mini-réacteur catalytique triphasique intensifié continu. Une stratégie de contrôle à deux couches (optimisation et contrôle) est utilisée pour contrôler la température et la concentration du produit à la sortie du réacteur en présence de perturbations à l'entrée du réacteur. Les performances du contrôleur mis en place sont comparées en simulation à celles d'un régulateur PI. Dans certains cas, l'utilisation de la fonction de disponibilité thermodynamique s'avère problématique. Une autre étude effectuée sur cette fonction nous permet de déterminer une nouvelle fonction de Lyapunov : la disponibilité thermique. Nous utilisons par la suite la fonction de disponibilité thermique pour la synthèse de lois de commande stabilisante d'un réacteur catalytique triphasique semi-fermé. Un observateur grand gain est utilisé pour estimer la vitesse de réaction à partir des mesures de la température du milieu réactionnel. Cette estimation est injectée ensuite dans le calcul de la loi de commande mise en place. La robustesse du schéma de contrôle est testée en simulation face à des incertitudes de modélisation, des perturbations et des bruits de mesure.
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Ferrer, Esteban. "A high order Discontinuous Galerkin - Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes for simulating cross-flow turbines." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:db8fe6e3-25d0-4f6a-be1b-6cde7832296d.
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This thesis details the development, verification and validation of an unsteady unstructured high order (≥ 3) h/p Discontinuous Galerkin - Fourier solver for the incompressible Navier-Stokes equations on static and rotating meshes in two and three dimensions. This general purpose solver is used to provide insight into cross-flow (wind or tidal) turbine physical phenomena. Simulation of this type of turbine for renewable energy generation needs to account for the rotational motion of the blades with respect to the fixed environment. This rotational motion implies azimuthal changes in blade aero/hydro-dynamics that result in complex flow phenomena such as stalled flows, vortex shedding and blade-vortex interactions. Simulation of these flow features necessitates the use of a high order code exhibiting low numerical errors. This thesis presents the development of such a high order solver, which has been conceived and implemented from scratch by the author during his doctoral work. To account for the relative mesh motion, the incompressible Navier-Stokes equations are written in arbitrary Lagrangian-Eulerian form and a non-conformal Discontinuous Galerkin (DG) formulation (i.e. Symmetric Interior Penalty Galerkin) is used for spatial discretisation. The DG method, together with a novel sliding mesh technique, allows direct linking of rotating and static meshes through the numerical fluxes. This technique shows spectral accuracy and no degradation of temporal convergence rates if rotational motion is applied to a region of the mesh. In addition, analytical mappings are introduced to account for curved external boundaries representing circular shapes and NACA foils. To simulate 3D flows, the 2D DG solver is parallelised and extended using Fourier series. This extension allows for laminar and turbulent regimes to be simulated through Direct Numerical Simulation and Large Eddy Simulation (LES) type approaches. Two LES methodologies are proposed. Various 2D and 3D cases are presented for laminar and turbulent regimes. Among others, solutions for: Stokes flows, the Taylor vortex problem, flows around square and circular cylinders, flows around static and rotating NACA foils and flows through rotating cross-flow turbines, are presented.
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Gunaydin, Zekiye. "Analysis And Design Of A Cuk Switching Regulator." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610606/index.pdf.
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This theses analyzes Cuk converter, that is one of the dc to dc switching converters. For continuous inductor current mode and discontinuous inductor current mode, stedy state operation is analysied. Characteristic parameters are determined. Through State Space Averge Models, Small Signal Models are obtained. Parasitic Resistance effects on steady state and small signal models are determined. Efficency of the switching converter is derived. Open loop transfer functions for continous and discontinuous inductor curret mode are obtained. Parmeters for small signal behaviour is determined and stability is analysied. Parasitic resistance effects on transfer functions is determined. Therotecial analysis are verified with a simulations of designed converter.
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Pena, Ismael da Silva. "Análise de estabilidade de sistemas dinâmicos híbridos e descontínuos modelados por semigrupos /." São José do Rio Preto : [s.n.], 2008. http://hdl.handle.net/11449/94205.
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Resumo: Sistemas dinâmicos híbridos se diferenciam por exibir simultaneamente variados tipos de comportamento dinâmico (contínuo, discreto, eventos discretos) em diferentes partes do sistema. Neste trabalho foram estudados resultados de estabilidade no sentido de Lyapunov para sistemas dinâmicos híbridos gerais, que utilizam uma noção de tempo generalizado, definido em um espaço métrico totalmente ordenado. Mostrou-se que estes sistemas podem ser imersos em sistemas dinâmicos descontínuos definidos em R+, de forma que sejam preservadas suas propriedades qualitativas. Como foco principal, estudou-se resultados de estabilidade para sistemas dinâmicos descontínuos modelados por semigrupos de operadores, em que os estados do sistema pertencem à espaços de Banach. Neste caso, de forma alternativa à teoria clássica de estabilidade, os resultados não utilizam as usuais funções de Lyapunov, sendo portanto mais fáceis de se aplicar, tendo em vista a dificuldade em se encontrar tais funções para muitos sistemas. Além disso, os resultados foram aplicados à uma classe de equações diferenciais com retardo.Abstract: Hybrid dynamical systems are characterized for showing simultaneously a variety of dynamic behaviors (continuous, discrete, discrete events) in different parts of the System. This work discusses stability results in the Lyapunov sense for general hybrid dynamical systems that use a generalized notion of time, defined in a completely ordered metric space. It has been shown that these systems may be immersed in discontinuous dynamical systems defined in R+, so that their quality properties are preserved. As the main focus, it is studied stability results for discontinuous dynamical systems modeled by semigroup operators, in which the states belong to Banach spaces. In this case, an alternative to the classical theory of stability, the results do not make use of the usual Lyapunov functions, and therefore are easier to apply, in view of the difficulty in finding such functions for many systems. Furthermore, the results were applied to a class of time-delay discontinuous differential equations.
Orientador: Geraldo Nunes Silva
Coorientador: Luís Antônio Fernandes de Oliveira
Banca: Carlos Alberto Raposo da Cunha
Banca: Waldemar Donizete Bastos
Mestre
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Pena, Ismael da Silva [UNESP]. "Análise de estabilidade de sistemas dinâmicos híbridos e descontínuos modelados por semigrupos:." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/94205.
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Sistemas dinâmicos híbridos se diferenciam por exibir simultaneamente variados tipos de comportamento dinâmico (contínuo, discreto, eventos discretos) em diferentes partes do sistema. Neste trabalho foram estudados resultados de estabilidade no sentido de Lyapunov para sistemas dinâmicos híbridos gerais, que utilizam uma noção de tempo generalizado, definido em um espaço métrico totalmente ordenado. Mostrou-se que estes sistemas podem ser imersos em sistemas dinâmicos descontínuos definidos em R+, de forma que sejam preservadas suas propriedades qualitativas. Como foco principal, estudou-se resultados de estabilidade para sistemas dinâmicos descontínuos modelados por semigrupos de operadores, em que os estados do sistema pertencem à espaços de Banach. Neste caso, de forma alternativa à teoria clássica de estabilidade, os resultados não utilizam as usuais funções de Lyapunov, sendo portanto mais fáceis de se aplicar, tendo em vista a dificuldade em se encontrar tais funções para muitos sistemas. Além disso, os resultados foram aplicados à uma classe de equações diferenciais com retardo.
Hybrid dynamical systems are characterized for showing simultaneously a variety of dynamic behaviors (continuous, discrete, discrete events) in different parts of the System. This work discusses stability results in the Lyapunov sense for general hybrid dynamical systems that use a generalized notion of time, defined in a completely ordered metric space. It has been shown that these systems may be immersed in discontinuous dynamical systems defined in R+, so that their quality properties are preserved. As the main focus, it is studied stability results for discontinuous dynamical systems modeled by semigroup operators, in which the states belong to Banach spaces. In this case, an alternative to the classical theory of stability, the results do not make use of the usual Lyapunov functions, and therefore are easier to apply, in view of the difficulty in finding such functions for many systems. Furthermore, the results were applied to a class of time-delay discontinuous differential equations.
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Gdhami, Asma. "Méthodes isogéométriques pour les équations aux dérivées partielles hyperboliques." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4210/document.
Full textAbstract:
L’Analyse isogéométrique (AIG) est une méthode innovante de résolution numérique des équations différentielles, proposée à l’origine par Thomas Hughes, Austin Cottrell et Yuri Bazilevs en 2005. Cette technique de discrétisation est une généralisation de l’analyse par éléments finis classiques (AEF), conçue pour intégrer la conception assistée par ordinateur (CAO), afin de combler l’écart entre la description géométrique et l’analyse des problèmes d’ingénierie. Ceci est réalisé en utilisant des B-splines ou des B-splines rationnelles non uniformes (NURBS), pour la description des géométries ainsi que pour la représentation de champs de solutions inconnus.L’objet de cette thèse est d’étudier la méthode isogéométrique dans le contexte des problèmes hyperboliques en utilisant les fonctions B-splines comme fonctions de base. Nous proposons également une méthode combinant l’AIG avec la méthode de Galerkin discontinue (GD) pour résoudre les problèmes hyperboliques. Plus précisément, la méthodologie de GD est adoptée à travers les interfaces de patches, tandis que l’AIG traditionnelle est utilisée dans chaque patch. Notre méthode tire parti de la méthode de l’AIG et la méthode de GD.Les résultats numériques sont présentés jusqu’à l’ordre polynomial p= 4 à la fois pour une méthode deGalerkin continue et discontinue. Ces résultats numériques sont comparés pour un ensemble de problèmes de complexité croissante en 1D et 2DIsogeometric Analysis (IGA) is a modern strategy for numerical solution of partial differential equations, originally proposed by Thomas Hughes, Austin Cottrell and Yuri Bazilevs in 2005. This discretization technique is a generalization of classical finite element analysis (FEA), designed to integrate Computer Aided Design (CAD) and FEA, to close the gap between the geometrical description and the analysis of engineering problems. This is achieved by using B-splines or non-uniform rational B-splines (NURBS), for the description of geometries as well as for the representation of unknown solution fields.The purpose of this thesis is to study isogeometric methods in the context of hyperbolic problems usingB-splines as basis functions. We also propose a method that combines IGA with the discontinuous Galerkin(DG)method for solving hyperbolic problems. More precisely, DG methodology is adopted across the patchinterfaces, while the traditional IGA is employed within each patch. The proposed method takes advantageof both IGA and the DG method.Numerical results are presented up to polynomial order p= 4 both for a continuous and discontinuousGalerkin method. These numerical results are compared for a range of problems of increasing complexity,in 1D and 2D
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Estecahandy, Elodie. "Contribution à l'analyse mathématique et à la résolution numérique d'un problème inverse de scattering élasto-acoustique." Phd thesis, Université de Pau et des Pays de l'Adour, 2013. http://tel.archives-ouvertes.fr/tel-00880628.
Full textAbstract:
La détermination de la forme d'un obstacle élastique immergé dans un milieu fluide à partir de mesures du champ d'onde diffracté est un problème d'un vif intérêt dans de nombreux domaines tels que le sonar, l'exploration géophysique et l'imagerie médicale. A cause de son caractère non-linéaire et mal posé, ce problème inverse de l'obstacle (IOP) est très difficile à résoudre, particulièrement d'un point de vue numérique. De plus, son étude requiert la compréhension de la théorie du problème de diffraction direct (DP) associé, et la maîtrise des méthodes de résolution correspondantes. Le travail accompli ici se rapporte à l'analyse mathématique et numérique du DP élasto-acoustique et de l'IOP. En particulier, nous avons développé un code de simulation numérique performant pour la propagation des ondes associée à ce type de milieux, basé sur une méthode de type DG qui emploie des éléments finis d'ordre supérieur et des éléments courbes à l'interface afin de mieux représenter l'interaction fluide-structure, et nous l'appliquons à la reconstruction d'objets par la mise en oeuvre d'une méthode de Newton régularisée.
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Lin, C. I., and 林敬穎. "Application of Describing Function to Estimate the Continuous and Discontinuous Conduction Mode for Converter." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/66567995772049872346.
Full textAbstract:
碩士逢甲大學
自動控制工程學系
89
For a dc-to-dc buck converter , the performance of the conductor is significantly different for the converter operating on the continuous conduction mode (CCM) or discontinuous conduction mode (DCM). In this paper, we address the operating condition on the CCM and DCM for a saturated inductor. I will show that the inductor plays a essential role for the converter operating on the CCM and DCM. It is known that when the load is large, the inductance for the inductor always changes. This is due to the fact that when the current load is large, the inductance always suffer from saturation or hysteresis. Because the inductance is nonlinear, it is very difficult to estimate the actual value for the nonlinear inductance during large current situations. With the dual-input describing function method, we can linearize the nonlinear inductor and then estimate the inductance during the large current situations. It can be shown that when the inductance of the inductor is saturated, the operating region of discontinuous conduction mode (DCM) of the buck converter will extent drastically, which means the converter will easily operate in the discontinuous conduction mode. A experimental example will verified these results.
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Wang, Shih-cheng, and 王士誠. "Iterative Learning Control of MIMO Linear System under Control Constraint Based on Sign Function for Discontinuous References." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/45594403388687885096.
Full textAbstract:
碩士國立成功大學
電機工程學系碩博士班
96
In view of the optimal control whose control input signal is very large in the thesis, we present a sign function algorithm based on the foundation of optimal control using linear quadratic regulator and high gain property to get an input saturation value, and supplies a good tracking performance. Then, take this good control input to be as first iteration of open loop iterative learning controller, it can get as well as performance in the first training iteration, and supplies a good tracking performance in both the transient and steady-state phase. Moreover, the method improves convergence and input saturation value in traditional iteration learning control. Besides, we present a method to overcome discontinuous and non-differentiable function in iterative learning control update rule, using Taylor series expansion to approach a correct value. Finally, MIMO numerical example is given to illustrate the effectiveness and the feasibility of the proposed method.
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Liao, Cheng-Mao, and 廖承茂. "Estimation of Discontinuous Regression Functions." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/15501520624699844067.
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"On the discontinuity of the Shannon information measures and typical sequences." Thesis, 2006. http://library.cuhk.edu.hk/record=b6074290.
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As entropy is also an important quantity in physics, we relate our results to physical processes by demonstrating that the discontinuity of entropy can occur in a Markov chain. We also discuss the possible implications of this phenomenon in thermodynamics and cosmology.For two probability distributions with finite alphabets, some bounds on the difference of their entropies as a function of their alphabet sizes and variational distance are obtained. These bounds, which are tighter than some existing results, show that entropy estimation by finite alphabet approximation may not work as we expected. On the other hand, we show that there always exists a finite alphabet approximation that works for entropy estimation provided that the alphabet used is sufficiently large. Some necessary and sufficient conditions under which the entropy of a sequence of probability distributions converges are given in terms of four new information divergence measures, where the square root of two of them are metrics.
In information theory, weak typicality and strong typicality are essential tools for proving coding theorems. Strong typicality, which is more powerful than weak typicality, can be applied to finite alphabet only, while weak typicality can be applied to both finite and countably infinite alphabets. We introduce a unified typicality for finite or countably infinite alphabet which is stronger than both weak typicality and strong typicality. With this unified typicality, the asymptotic equipartition property and the structural properties of strong typicality are preserved.
The Shannon information measures are well known to be continuous functions of the probability distribution for finite alphabet. In this thesis, however, we show that these measures are discontinuous with respect to almost all commonly used "distance" measures when the alphabet is countably infinite. Such "distance" measures include the Kullback-Leibler divergence and the variational distance. Specifically, we show that all the Shannon information measures are in fact discontinuous at all probability distributions.
Ho Siu Wai.
"August 2006."
Adviser: Wai Ho Raymond Yeung.
Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1824.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2006.
Includes bibliographical references (p. 121-123).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts in English and Chinese.
School code: 1307.
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Hsu, Chen-Ming, and 許振銘. "WildSpan : Discovery of Discontinuous Functional Motifs from Protein Sequences." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/75922920449230580109.
Full textAbstract:
博士元智大學
資訊工程學系
95
As more and more protein sequences is increasing exponentially with their structures undetermined, recognizing functional signatures directly from sequences is particularly desirable in functional proteomics. Automatic extraction of motifs from biological sequences is one of central problems in molecular biology. For proteins, identifying sequence motifs that contain large irregular gaps is important as the contact residues that are associated with a functional site are not always from one region of the sequence. Discovering such patterns is time-consuming because a large number of combinations exist when large and flexible wildcards (gaps) are considered. To tackle the efficiency issue, mining algorithms often employ constraints to narrow down the search space and thus increase efficiency. However, improper constraint models degrade the sensitivity and specificity of the algorithms. Designing efficient and effective algorithms to discover discontinuous functional motifs is the theme of this dissertation. In this dissertation we propose a new constraint model and accordingly design a novel algorithm, WildSpan, to efficiently and effectively handle wide-range flexible-width wildcard regions. WildSpan employs a number of pruning strategies during pattern (motif) search, and ensures that only compactly representative patterns (closed patterns) are reported. The experimental results reveal that WildSpan is efficient and effective in discovering functional signatures of proteins directly from sequences. Furthermore, the idea of WildSpan was realized on the web server MAGIIC-PRO to provide an easy-to-use environment in that the users can easily collect training data and the derived patterns can be examined through several well-developed facilities.
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Hsu, Mong-Da, and 徐孟達. "Effects of Continuous and Discontinuous Running Exercise on Cortisol and Immune Functions." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/34773145727411521655.
Full textAbstract:
博士國立臺灣師範大學
體育研究所
90
Purpose: The purpose of this study was to examine the effects of continuous and discontinuous running exercise on cortisol and immune functions. Method: Thirty university male students (age=20.80±1.49 years, VO2max values=44.57±6.23 ml/min-1．kg-1) were recruited as the subjects for this study. They were divided into three different groups according to VO2max values: continuous exercise group (CEG), discontinuous exercise group (DEG) and control group (CG). The CEG performed single bout of treadmill exercise lasting 30 minutes at 70% VO2R at 13:00 (3 times/wk, 1wk). The DEG performed two bouts of treadmill exercise lasting 15 minutes at 70% VO2R at 9:00 and 13:15 (3 times/wk, 1wk). Blood samples were collected at rest before exercise, 0 hour, 2 hours and 24 hours after exercise. Cortisol, leucocyte count, neutrophil count, lymphocyte count, peripheral mononuclear cell (PMNC) proliferation, and cytokines were measured. Data were analyzed using mixed design two-way ANOVA and repeated one-way ANOVA. Results: 1) Circadian rhythm could influence cortisol concentration significantly, but there was no difference on cortisol between each group. 2) Leucocyte count, neutrophil count, lymphocyte count of CEG were significantly higher, but PMNC proliferation was lower (p< .05) at 0 hour after exercise than the DEG and CG. 2) Neutrophil count of CEG was still higher, but lymphocyte count was lower (p< .05) at 2 hours after exercise than the other groups. 3) There was no difference on cytokines between each group. Conclusions: Circadian rhythm could influence cortisol concentration significantly. During the whole period of testing, the lymphocyte count and PMNC proliferation of CEG were lower within two hours after exercise and may temporarily depress the subjects’ immune function. However, the subjects of DEG and CG didn’t show any depression of the immune variables after exercise.
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Jakeman, John Davis. "Numerical methods for the quantification of uncertainty in discontinuous functions of high dimension." Phd thesis, 2011. http://hdl.handle.net/1885/150999.
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Bramwell, Jamie Ann. "A discontinuous Petrov-Galerkin method for seismic tomography problems." 2013. http://hdl.handle.net/2152/21979.
Full textAbstract:
The imaging of the interior of the Earth using ground motion data, or seismic tomography, has been a subject of great interest for over a century. The full elastic wave equations are not typically used in standard tomography codes. Instead, the elastic waves are idealized as rays and only phase velocity and travel times are considered as input data. This results in the inability to resolve features which are on the order of one wavelength in scale. To overcome this problem, models which use the full elastic wave equation and consider total seismograms as input data have recently been developed. Unfortunately, those methods are much more computationally expensive and are only in their infancy. While the finite element method is very popular in many applications in solid mechanics, it is still not the method of choice in many seismic applications due to high pollution error. The pollution effect creates an increasing ratio of discretization to best approximation error for problems with increasing wave numbers. It has been shown that standard finite element methods cannot overcome this issue. To compensate, the meshes for solving high wave number problems in seismology must be increasingly refined, and are computationally infeasible due to the large scale requirements. A new generalized least squares method was recently introduced. The main idea is to select test spaces such that the discrete problem inherits the stability of the continuous problem. In this dissertation, a discontinuous Petrov-Galerkin method with optimal test functions for 2D time-harmonic seismic tomography problems is developed. First, the abstract DPG framework and key results are reviewed. 2D DPG methods for both static and time-harmonic elasticity problems are then introduced and results indicating the low-pollution property are shown. Finally, a matrix-free inexact-Newton method for the seismic inverse problem is developed. To conclude, results obtained from both DPG and standard continuous Galerkin discretization schemes are compared and the potential effectiveness of DPG as a practical seismic inversion tool is discussed.text
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Balázsová, Monika. "Některé aspekty nespojité Galerkinovy metody pro řešení konvektivně-difuzních problémů." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-321440.
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In the present work we deal with the stability of the space-time discontinuous Galerkin method applied to non-stationary, nonlinear convection - diffusion problems. Discontinuous Galerkin method is a very efficient tool for numerical solution of partial differential equations, combines the advantages of the finite element method (polynomial approximations of high order of accuracy) and the finite volume method (discontinuous approximations). After the formulation of the continuous problem its discretization in space and time is described. In the formulation of the discontinuous Galerkin method the non-symmetric, symmetric and incomplete version of discretization of the diffusion term is used and there are added penalty terms to the scheme also. In the third chapter are estimated individual terms of the previously derived approximate solution by special norms. Using the concept of discrete characteristic functions and the discrete Gronwall lemma, it is shown that the analyzed scheme is unconditionally stable. At the end, in the fourth chapter, are given some numerical experiments, which verify theoretical results from the previous chapter.
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Литвин, О. М., О. Г. Литвин, and О. О. Литвин. "Method of Calculating Fourier Coefficients of Three Variable Functions Using Tomogram." Thesis, 2019. http://openarchive.nure.ua/handle/document/9457.
Full textAbstract:
A method for calculating Fourier coefficients of functions of three variables using tomograms is proposed and
investigated. Earlier Lytvyn O.M. proposed and introduced the method of calculating Fourier coefficients of the function of two variables using integrals of this function along a given system of direct. It is believed that these integrals - projections or projection data arrive from a computer tomograph.
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Chan, Jesse L. "A DPG method for convection-diffusion problems." 2013. http://hdl.handle.net/2152/21417.
Full textAbstract:
Over the last three decades, CFD simulations have become commonplace as a tool in the engineering and design of high-speed aircraft. Experiments are often complemented by computational simulations, and CFD technologies have proved very useful in both the reduction of aircraft development cycles, and in the simulation of conditions difficult to reproduce experimentally. Great advances have been made in the field since its introduction, especially in areas of meshing, computer architecture, and solution strategies. Despite this, there still exist many computational limitations in existing CFD methods; in particular, reliable higher order and hp-adaptive methods for the Navier-Stokes equations that govern viscous compressible flow. Solutions to the equations of viscous flow can display shocks and boundary layers, which are characterized by localized regions of rapid change and high gradients. The use of adaptive meshes is crucial in such settings -- good resolution for such problems under uniform meshes is computationally prohibitive and impractical for most physical regimes of interest. However, the construction of "good" meshes is a difficult task, usually requiring a-priori knowledge of the form of the solution. An alternative to such is the construction of automatically adaptive schemes; such methods begin with a coarse mesh and refine based on the minimization of error. However, this task is difficult, as the convergence of numerical methods for problems in CFD is notoriously sensitive to mesh quality. Additionally, the use of adaptivity becomes more difficult in the context of higher order and hp methods. Many of the above issues are tied to the notion of robustness, which we define loosely for CFD applications as the degradation of the quality of numerical solutions on a coarse mesh with respect to the Reynolds number, or nondimensional viscosity. For typical physical conditions of interest for the compressible Navier-Stokes equations, the Reynolds number dictates the scale of shock and boundary layer phenomena, and can be extremely high -- on the order of 10⁷ in a unit domain. For an under-resolved mesh, the Galerkin finite element method develops large oscillations which prevent convergence and pollute the solution. The issue of robustness for finite element methods was addressed early on by Brooks and Hughes in the SUPG method, which introduced the idea of residual-based stabilization to combat such oscillations. Residual-based stabilizations can alternatively be viewed as modifying the standard finite element test space, and consequently the norm in which the finite element method converges. Demkowicz and Gopalakrishnan generalized this idea in 2009 by introducing the Discontinous Petrov-Galerkin (DPG) method with optimal test functions, where test functions are determined such that they minimize the discrete linear residual in a dual space. Under the ultra-weak variational formulation, these test functions can be computed locally to yield a symmetric, positive-definite system. The main theoretical thrust of this research is to develop a DPG method that is provably robust for singular perturbation problems in CFD, but does not suffer from discretization error in the approximation of test functions. Such a method is developed for the prototypical singular perturbation problem of convection-diffusion, where it is demonstrated that the method does not suffer from error in the approximation of test functions, and that the L² error is robustly bounded by the energy error in which DPG is optimal -- in other words, as the energy error decreases, the L² error of the solution is guaranteed to decrease as well. The method is then extended to the linearized Navier-Stokes equations, and applied to the solution of the nonlinear compressible Navier-Stokes equations. The numerical work in this dissertation has focused on the development of a 2D compressible flow code under the Camellia library, developed and maintained by Nathan Roberts at ICES. In particular, we have developed a framework allowing for rapid implementation of problems and the easy application of higher order and hp-adaptive schemes based on a natural error representation function that stems from the DPG residual. Finally, the DPG method is applied to several convection diffusion problems which mimic difficult problems in compressible flow simulations, including problems exhibiting both boundary layers and singularities in stresses. A viscous Burgers' equation is solved as an extension of DPG to nonlinear problems, and the effectiveness of DPG as a numerical method for compressible flow is assessed with the application of DPG to two benchmark problems in supersonic flow. In particular, DPG is used to solve the Carter flat plate problem and the Holden compression corner problem over a range of Mach numbers and laminar Reynolds numbers using automatically adaptive schemes, beginning with very under-resolved/coarse initial meshes.text