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1
Berry, Matthew M. "A Variable-Step Double-Integration Multi-Step Integrator." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11155.
Повний текст джерелаАнотація:
A new method of numerical integration is presented here, the variable-step Stormer-Cowell method. The method uses error control to regulate the step size, so larger step sizes can be taken when possible, and is double-integration, so only one evaluation per step is necessary when integrating second-order differential equations. The method is not variable-order, because variable-order algorithms require a second evaluation.
The variable-step Stormer-Cowell method is designed for space surveillance applications,which require numerical integration methods to track orbiting objects accurately. Because of the large number of objects being processed, methods that can integrate the equations of motion as fast as possible while maintaining accuracy requirements are desired. The force model used for earth-orbiting objects is quite complex and computationally expensive, so methods that minimize the force model evaluations are needed.
The new method is compared to the fixed-step Gauss-Jackson method, as well as a method of analytic step regulation (s-integration), and the variable-step variable-order Shampine-Gordon integrator. Speed and accuracy tests of these methods indicate that the new method is comparable in speed and accuracy to s-integration in most cases, though the variable-step Stormer-Cowell method has an advantage over s-integration when drag is a significant factor. The new method is faster than the Shampine-Gordon integrator, because the Shampine-Gordon integrator uses two evaluations per step, and is biased toward keeping the step size constant. Tests indicate that both the new variable-step Stormer-Cowell method and s-integration have an advantage over the fixed-step Gauss-Jackson method for orbits with eccentricities greater than 0.15.Ph. D.
2
Lastdrager, Boris. "Numerical time integration on sparse grids." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2002. http://dare.uva.nl/document/64526.
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3
Ou, Rongfu. "Parallel numerical integration methods for nonlinear dynamics." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/18181.
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4
Akinola, Richard Olatokunbo. "Numerical indefinite integration using the sinc method." Thesis, Link to the online version, 2007. http://hdl.handle.net/10019/1049.
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5
Alsallami, Shami Ali M. "Discrete integrable systems and geometric numerical integration." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/22291/.
Повний текст джерелаАнотація:
This thesis deals with discrete integrable systems theory and modified Hamiltonian equations in the field of geometric numerical integration. Modified Hamiltonians are used to show that symplectic schemes for Hamiltonian systems are accurate over long times. However, for nonlinear systems the series defining the modified Hamiltonian equation usually diverges. The first part of the thesis demonstrates that there are nonlinear systems where the modified Hamiltonian has a closed-form expression and hence converges. These systems arise from the theory of discrete integrable systems. Specifically, they arise as reductions of a lattice version of the Korteweg-de Vries (KdV) partial differential equation. We present cases of one and two degrees of freedom symplectic mappings, for which the modified Hamiltonian equations can be computed as a closed form expression using techniques of action-angle variables, separation of variables and finite-gap integration. These modified Hamiltonians are also given as power series in the time step by Yoshida's method based on the Baker-Campbell-Hausdorff series. Another example is a system of an implicit dependence on the time step, which is obtained by dimensional reduction of a lattice version of the modified KdV equation. The second part of the thesis contains a different class of discrete-time system, namely the Boussinesq type, which can be considered as a higher-order counterpart of the KdV type. The development and analysis of this class by means of the B{\"a}cklund transformation, staircase reductions and Dubrovin equations forms one of the major parts of the thesis. First, we present a new derivation of the main equation, which is a nine-point lattice Boussinesq equation, from the B{\"a}cklund transformation for the continuous Boussinesq equation. Second, we focus on periodic reductions of the lattice equation and derive all necessary ingredients of the corresponding finite-dimensional models. Using the corresponding monodromy matrix and applying techniques from Lax pair and $r$-matrix structure analysis to the Boussinesq mappings, we study the dynamics in terms of the so-called Dubrovin equations for the separated variables.
6
Strandberg, Rickard, and Johan Låås. "Uncertainty quantification using high-dimensional numerical integration." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-195701.
Повний текст джерелаАнотація:
We consider quantities that are uncertain because they depend on one or many uncertain parameters. If the uncertain parameters are stochastic the expected value of the quantity can be obtained by integrating the quantity over all the possible values these parameters can take and dividing the result by the volume of the parameter-space. Each additional uncertain parameter has to be integrated over; if the parameters are many, this give rise to high-dimensional integrals. This report offers an overview of the theory underpinning four numerical methods used to compute high-dimensional integrals: Newton-Cotes, Monte Carlo, Quasi-Monte Carlo, and sparse grid. The theory is then applied to the problem of computing the impact coordinates of a thrown ball by introducing uncertain parameters such as wind velocities into Newton’s equations of motion.
7
Tranquilli, Paul J. "Lightly-Implicit Methods for the Time Integration of Large Applications." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/81974.
Повний текст джерелаАнотація:
Many scientific and engineering applications require the solution of large systems of initial value problems arising from method of lines discretization of partial differential equations. For systems with widely varying time scales, or with complex physical dynamics, implicit time integration schemes are preferred due to their superior stability properties. However, for very large systems accurate solution of the implicit terms can be impractical. For this reason approximations are widely used in the implementation of such methods.
The primary focus of this work is on the development of novel ``lightly-implicit'' time integration methodologies. These methods consider the time integration and the solution of the implicit terms as a single computational process. We propose several classes of lightly-implicit methods that can be constructed to allow for different, specific approximations.
Rosenbrock-Krylov and exponential-Krylov methods are designed to permit low accuracy Krylov based approximations of the implicit terms, while maintaining full order of convergence. These methods are matrix free, have low memory requirements, and are particularly well suited to parallel architectures. Linear stability analysis of K-methods is leveraged to construct implementation improvements for both Rosenbrock-Krylov and exponential-Krylov methods.
Linearly-implicit Runge-Kutta-W methods are designed to permit arbitrary, time dependent, and stage varying approximations of the linear stiff dynamics of the initial value problem. The methods presented here are constructed with approximate matrix factorization in mind, though the framework is flexible and can be extended to many other approximations.
The flexibility of lightly-implicit methods, and their ability to leverage computationally favorable approximations makes them an ideal alternative to standard explicit and implicit schemes for large parallel applications.Ph. D.
8
Qureshi, Muhammad Amer. "Efficient numerical integration for gravitational N-body simulations." Thesis, University of Auckland, 2012. http://hdl.handle.net/2292/10826.
Повний текст джерелаАнотація:
Models for N-body gravitational simulations of the Solar System vary from small simulations of two bodies over short intervals of time to simulations of large numbers of bodies over long-term integration. Most simulations require the numerical solution of an initial value problem (IVP) of second-order ordinary differential equation. We present new integration methods intended for accurate simulations that are more efficient than existing methods. In the first part of the thesis, we present new higher-order explicit Runge–Kutta Nyström pairs. These new pairs are searched using a simulated annealing algorithm based on optimisation. The new pairs are up to approximately 60% more efficient than the existing ones. We implement these new pairs for a variety of gravitational problems and investigate the growth of global error in position for these problems along with relative error in conserved quantities. The second part consists of the implementation of the Gauss Implicit Runge-Kutta methods in an efficient way such that the error growth satisfies Brouwer’s Law. Numerical experiments show that using the new way of implementation reduces the integration cost up to 20%. We also implement continuous extensions for the Gauss implicit Runge-Kutta methods, using interpolation polynomials at nodal points.
9
Wang, Honghou 1963. "Practical adaptive numerical integration for finite element electromagnetics." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=30277.
Повний текст джерелаАнотація:
Currently, several numerical methods have been provided for 2-D and 3-D integrations. But there is insufficient analysis reported on the overall performances of the available methods for fundamental electromagnetics problems. A complete evaluation is presented to discover the best ways of integrating these electromagnetics problems through benchmark performance studies of the available methods focussing on the integration accuracy, the location of sampling points, and the influence of integration domain refinement schemes. To meet this goal, three benchmark problems have been designed and evaluated. Accurate and reasonably cost-efficient integration methods are recommended.
10
Oliva, Federico. "Modelling, stability, and control of DAE numerical integration." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20143/.
Повний текст джерелаАнотація:
This thesis deals with the integration of differential algebraic equations systems. Generally speaking the execution of numerical integration algorithms may introduce some errors, which could propagate ending up in a wrong description of system dynamics. This issue, named drifting, will be highlighted by dealing with a specific constrained mechanical system presenting. Such system consists of a looper, which is a mechanism used in the steel production to sense and control the tension acting on the material. The thesis unfolds as follows: a first section model the looper and inspects the main properties related to its joint space and singularities. A brief introduction to stability analysis on multidof systems is proposed. Then, the thesis proceeds analysing looper stability properties, eventually finding a globally asymptotic stable configuration. Lastly, the drifting is highlighted by numerical simulations. To solve this issue two control algorithms are proposed: the first is the Baumgarte algorithm and the second consists of a nonlinear stabilizer. A performance comparison of both algorithms is then presented at the end of the implementation description.
11
Thompson, Jeremy Stewart. "High speed numerical integration of Fermi Dirac integrals." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1996. http://handle.dtic.mil/100.2/ADA311805.
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12
Wang, Honghou. "Practical adaptive numerical integration for finite element electromagnetics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0030/MQ64253.pdf.
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13
Webster, Jonathan Robert. "Methods of numerical integration for rapidly oscillatory integrals." Thesis, Loughborough University, 1999. https://dspace.lboro.ac.uk/2134/13776.
Повний текст джерелаАнотація:
This thesis is concerned with the evaluation of rapidly oscillatory integrals, that is integrals in which the integrand has numerous local maxima and minima over the range of integration. Three numerical integration rules are presented. The first is suitable for computing rapidly oscillatory integrals with trigonometric oscillations of the form f(x) exp(irq(x)). The method is demonstrated, empirically, to be convergent and numerically stable as the order of the formula is increased. For other forms of oscillatory behaviour, a second approach based on Lagrange's identity is presented. The technique is suitable for any oscillatory weight function, provided that it satisfies an ordinary linear differential equation of order m :2:: 1. The method is shown to encompass Bessel oscillations, trigonometric oscillations and Fresnel oscillations, and products of these terms. Examples are included which illustrate the efficiency of the method in practical applications. Finally, integrals where the integrand is singular and oscillatory are considered. An extended Clenshaw-Curtis formula is developed for Fourier integrals which exhibit algebraic and logarithmic singularities. An efficient algorithm is presented for the practical implementation of the method.
14
Shaw, J. E. H. "Numerical integration and display methods for Bayesian inference." Thesis, University of Nottingham, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233374.
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15
CAMPAGNOLO, LEONARDO QUATRIN. "ACCURATE VOLUME RENDERING BASED ON ADAPTIVE NUMERICAL INTEGRATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25693@1.
Повний текст джерелаАнотація:
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Um dos principais desafios em algoritmos de visualização volumétrica é calcular a integral volumétrica de maneira eficiente, mantendo uma precisão mínima adequada. Geralmente, métodos de integração numérica utilizam passos de tamanho constante, não incluindo nenhuma estratégia de controle numérico. Como uma possível solução, métodos numéricos adaptativos podem ser utilizados, pois conseguem adaptar o tamanho do passo de integração dada uma tolerância de erro pré-definida. Em CPU, os algoritmos adaptativos de integração numérica são, normalmente, implementados recursivamente. Já em GPU, é desejável eliminar implementações recursivas. O presente trabalho propõe um algoritmo adaptativo e iterativo para a avaliação da integral volumétrica em malhas regulares, apresentando soluções para manter o controle do passo da integral interna e externa. Os resultados do trabalho buscaram comparar a precisão e eficiência do método proposto com o modelo de integração com passo de tamanho constante, utilizando a soma de Riemann. Verificou-se que o algoritmo proposto gerou resultados precisos, com desempenho competitivo. As comparações foram feitas em CPU e GPU.
One of the main challenges in volume rendering algorithms is how to compute the Volume Rendering Integral accurately, while maintaining good performance. Commonly, numerical methods use equidistant samples to approximate the integral and do not include any error estimation strategy to control accuracy. As a solution, adaptive numerical methods can be used, because they can adapt the step size of the integration according to an estimated numerical error. On CPU, adaptive integration algorithms are usually implemented recursively. On GPU, however, it is desirable to eliminate recursive algorithms. In this work, an adaptive and iterative integration strategy is presented to evaluate the volume rendering integral for regular volumes, maintaining the control of the step size for both internal and external integrals. A set of computational experiments were made comparing both accuracy and efficiency against the Riemann summation with uniform step size. The proposed algorithm generates accurate results, with competitive performance. The comparisons were made using both CPU and GPU implementations.
16
Barrett, Michael Ian. "Numerical integration routines for the Gest simulation environment." Thesis, University of Ottawa (Canada), 1988. http://hdl.handle.net/10393/5500.
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17
Klapproth, Corinna [Verfasser]. "Adaptive numerical integration of dynamical contact problems / Corinna Klapproth." Berlin : Freie Universität Berlin, 2011. http://d-nb.info/1025490290/34.
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18
Mo, Eirik. "Nonlinear stochastic dynamics and chaos by numerical path integration." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-1786.
Повний текст джерелаАнотація:
The numerical path integration method for solving stochastic differential equations is extended to solve systems up to six spatial dimensions, angular variables, and highly nonlinear systems - including systems that results in discontinuities in the response probability density function of the system. Novel methods to stabilize the numerical method and increase computation speed are presented and discussed. This includes the use of the fast Fourier transform (FFT) and some new spline interpolation methods. Some sufficient criteria for the path integration theory to be applicable is also presented. The development of complex numerical code is made possible through automatic code generation by scripting. The resulting code is applied to chaotic dynamical systems by adding a Gaussian noise term to the deterministic equation. Various methods and approximations to compute the largest Lyapunov exponent of these systems are presented and illustrated, and the results are compared. Finally, it is shown that the location and size of the additive noise term affects the results, and it is shown that additive noise for specific systems could make a non-chaotic system chaotic, and a chaotic system non-chaotic.
19
Kleppe, Tore Selland. "Numerical Path Integration for Lévy Driven Stochastic Differential Equations." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2006. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9293.
Повний текст джерелаАнотація:
Some theory on Lévy processes and stochastic differential equations driven by Lévy processes is reviewed. Inverse Fast Fourier Transform routines are applied to compute the density of the increments of Lévy processes. We look at exact and approximate path integration operators to compute the probability density function of the solution process of a given stochastic differential equation. The numerical path integration method is shown to converge under the transition kernel backward convergence assumption. The numerical path integration method is applied on several examples with non-Brownian driving noises and nonlinearities, and shows satisfactory results. In the case when the noise is of additive type, a general code written for Lévy driving noises specified by the Lévy-Khintchine formula is described. A preliminary result on path integration in Fourier space is given.
20
Gil, Gibin. "Hybrid Numerical Integration Scheme for Highly Oscillatory Dynamical Systems." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/306771.
Повний текст джерелаАнотація:
Computational efficiency of solving the dynamics of highly oscillatory systems is an important issue due to the requirement of small step size of explicit numerical integration algorithms. A system is considered to be highly oscillatory if it contains a fast solution that varies regularly about a slow solution. As for multibody systems, stiff force elements and contacts between bodies can make a system highly oscillatory. Standard explicit numerical integration methods should take a very small step size to satisfy the absolute stability condition for all eigenvalues of the system and the computational cost is dictated by the fast solution. In this research, a new hybrid integration scheme is proposed, in which the local linearization method is combined with a conventional integration method such as the fourth-order Runge-Kutta. In this approach, the system is partitioned into fast and slow subsystems. Then, the two subsystems are transformed into a reduced and a boundary-layer system using the singular perturbation theory. The reduced system is solved by the fourth-order Runge-Kutta method while the boundary-layer system is solved by the local linearization method. This new hybrid scheme can handle the coupling between the fast and the slow subsystems efficiently. Unlike other multi-rate or multi-method schemes, extrapolation or interpolation process is not required to deal with the coupling between subsystems. Most of the coupling effect can be accounted for by the reduced (or quasi-steady-state) system while the minor transient effect is taken into consideration by averaging. In this research, the absolute stability region for this hybrid scheme is derived and it is shown that the absolute stability region is almost independent of the fast variables. Thus, the selection of the step size is not dictated by the fast solution when a highly oscillatory system is solved, in turn, the computational efficiency can be improved. The advantage of the proposed hybrid scheme is validated through several dynamic simulations of a vehicle system including a flexible tire model. The results reveal that the hybrid scheme can reduce the computation time of the vehicle dynamic simulation significantly while attaining comparable accuracy.
21
Dellaportas, Petros. "Imbedded integration rules and their applications in Bayesian analysis." Thesis, University of Plymouth, 1990. http://hdl.handle.net/10026.1/2067.
Повний текст джерелаАнотація:
This thesis deals with the development and application of numerical integration techniques for use in Bayesian Statistics. In particular, it describes how imbedded sequences of positive interpolatory integration rules (PIIR's) obtained from Gauss-Hermite product rules can extend the applicability and efficiency of currently available numerical methods. The numerical strategy suggested by Naylor and Smith (1982) is reviewed, criticised and applied to some examples with real and artificial data. The performance of this strategy is assessed from the viewpoint of 3 criteria: reliability, efficiency and accuracy. The imbedded sequences of PIIR’s are introduced as an alternative and an extension to the above strategy for two major reasons. Firstly, they provide a rich class of spatially ditributed rules which are particularly useful in high dimensions. Secondly, they provide a way of producing more efficient integration strategies by enabling approximations to be updated sequentially through the addition of new nodes at each step rather than through changing to a completely new set of nodes. Finally, the Improvement in the reliability and efficiency achieved by the adaption of an integration strategy based on PIIR's is demonstrated with various illustrative examples. Moreover, it is directly compared with the Gibbs sampling approach introduced recently by Gelfand and Smith (1988).
22
Dokchan, Rakporn. "Numerical integration of differential-algebraic equations with harmless critical points." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16318.
Повний текст джерелаАнотація:
Algebro-Differentialgleichungen (engl. differential-algebraic equations - DAEs) sind implizite singuläre gewöhnliche Differentialgleichungen, die restringierte dynamische Prozesse beschreiben. Sie unterscheiden sich von expliziten gewöhnlichen Differentialgleichungen dahingehend, dass Anfangswerte nicht beliebig vorgegeben werden können. Weiterhin sind in einer DAE neben Integrations- auch Differentiationsaufgaben involviert. Der Differentiationsindex gibt an, wieviele Differentiationen zur Lösung notwendig sind. Seit den 1980er Jahren wird vorwiegend an der Charakterisierung und Klassifizierung regulärer DAEs und der Konstruktion nebst Fundierung von Integrationsmethoden gearbeitet. I. Higueras, R. März und C. Tischendorf haben gezeigt, dass man lineare DAEs mit properem Hauptterm, A(t)(D(t)x(t))'' + B(t)x(t) = q(t), die regulär mit Traktabilitätsindex 2 sind, zuverlässig numerisch integrieren kann - im Unterschied zu linearen DAEs in Standardform. In Publikationen von R. Riaza und R. März wird die Klassifizierungen kritischer Punkten von linearen DAEs an die Verletzung bestimmter Rangbedingungen von Matrixfunktionen im Rahmen des Traktabilitätsindexes geknüpft. Im wesentlichen heißt ein kritischer Punkt harmlos, wenn der durch die inhärente Differentialgleichung beschriebene Fluß nicht tangiert ist. Gegenstand der vorliegenden Arbeit sind lineare quasi-proper formulierte DAEs. Es werden Index 2 DAEs mit harmlosen kritischen Punkten charakterisiert. Unter Verwendung von quasi-zulässigen Projektorfunktionen können neben DAEs, die fast überall gleiche charakteristische Werte haben, nun erstmalig auch solche mit Indexwechseln behandelt werden. Der Hauptteil der Arbeit besteht im Nachweis von Durchführbarkeit, Konvergenz und nur schwacher Instabilität von numerischen Integrationsmethoden (BDF, IRK(DAE)) für lineare Index 2 DAEs mit harmlosen kritischen Punkten, sowie in der Entwicklung von Fehlerschätzern und Schrittweitensteuerung.Differential-algebraic equations (DAEs) are implicit singular ordinary differential equations, which describe dynamical processes that are restricted by some constraints. In contrast to explicit regular ordinary differential equations, for a DAE not any value can be imposed as an initial condition. Furthermore, DAEs involve not only integration problems but also differentiation problems. The differentiation index of a DAE indicates the number of differentiations required in order to solve a DAE. Since the 1980th, research focuses primarily on the characterization and classification of regular problem classes and the construction and foundation of integration methods for simulation software. I. Higueras, R. Maerz, and C. Tischendorf have shown that one can reliably integrate a general linear DAE with a properly stated leading term, A(t)(D(t)x(t))'' + B(t)x(t) = q(t), which is regular with tractability index 2 - in contrast to linear standard form DAEs. The first classification of critical points of linear DAEs has been published by R. Riaza and R. Maerz. Based on the tractability index, critical points are classified according to failures of certain rank conditions of matrix functions. Essentially, a critical point is said to be harmless, if the flow described by the inherent differential equation is not affected. The subject of this work are quasi-proper linear DAEs. Index-2 DAEs with harmless critical points are characterized. Under the application of quasi-admissible projector functions. Besides DAEs which have almost everywhere the same characteristic values, DAEs with index changes can now be discussed for the first time. The main part of the work is to provide a proof of feasibility, convergence, and only weak instability of numerical integration methods (BDF, IRK (DAE)) for linear index-2 DAEs with harmless critical points, as well as the development and testing of error estimators and stepsize control.
23
Shearer, J. M. "Interval methods for non-linear systems." Thesis, University of St Andrews, 1986. http://hdl.handle.net/10023/13779.
Повний текст джерелаАнотація:
In numerical mathematics, there is a need for methods which provide a user with the solution to his problem without requiring him to understand the mathematics underlying the method of solution. Such a method involves computable tests to determine whether or not a solution exists in a given region, and whether, if it exists, such a solution may be found by using the given method. Two valuable tools for the implementation of such methods are interval mathematics and symbolic computation. In. practice all computers have memories of finite size and cannot perform exact arithmetic. Therefore, in addition to the error which is inherent in a given numerical method, namely truncation error, there is also the error due to rounding. Using interval arithmetic, computable tests which guarantee the existence of a solution to a given problem in a given region, and the convergence of a particular iterative method to this solution, become practically realizable. This is not possible using real arithmetic due to the accumulation of rounding error on a computer. The advent of packages which allow symbolic computations to be carried out on a given computer is an important advance for computational numerical mathematics. In particular, the ability to compute derivatives automatically removes the need for a user to supply them, thus eliminating a major source of error in the use of methods requiring first or higher derivatives. In this thesis some methods which use interval arithmetic and symbolic computation for the solution of systems of nonlinear algebraic equations are presented. Some algorithms based on the symmetric single-step algorithm are described. These methods however do not possess computable existence, uniqueness, and convergence tests. Algorithms which do possess such tests, based on the Krawczyk-Moore algorithm are also presented. A simple package which allows symbolic computations to be carried out is described. Several applications for such a package are given. In particular, an interval form of Brown's method is presented.
24
Fooladi, Samaneh, and Samaneh Fooladi. "Numerical Implementation of Elastodynamic Green's Function for Anisotropic Media." Thesis, The University of Arizona, 2016. http://hdl.handle.net/10150/623144.
Повний текст джерелаАнотація:
Displacement Green's function is the building block for some semi-analytical methods like Boundary Element Method (BEM), Distributed Point Source Method (DPCM), etc. In this thesis, the displacement Green`s function in anisotropic media due to a time harmonic point force is studied. Unlike the isotropic media, the Green's function in anisotropic media does not have a closed form solution. The dynamic Green's function for an anisotropic medium can be written as a summation of singular and non-singular or regular parts. The singular part, being similar to the result of static Green's function, is in the form of an integral over an oblique circular path in 3D. This integral can be evaluated either by a numerical integration technique or can be converted to a summation of algebraic terms via the calculus of residue. The other part, which is the regular part, is in the form of an integral over the surface of a unit sphere. This integral needs to be evaluated numerically and its evaluation is considerably more time consuming than the singular part. Obtaining dynamic Green's function and its spatial derivatives involves calculation of these two types of integrals. The spatial derivatives of Green's function are important in calculating quantities like stress and stain tensors. The contribution of this thesis can be divided into two parts. In the first part, different integration techniques including Gauss Quadrature, Simpson's, Chebyshev, and Lebedev integration techniques are tried out and compared for evaluation of dynamic Green’s function. In addition the solution from the residue theorem is included for the singular part. The accuracy and performance of numerical implementation is studied in detail via different numerical examples. Convergence plots are used to analyze the numerical error for both Green's function and its derivatives. The second part of contribution of this thesis relates to the mathematical derivations. As mentioned above, the regular part of dynamic Green's function, being an integral over the surface of a unit sphere, is responsible for the majority of computational time. From symmetry properties, this integration domain can be reduced to a hemisphere, but no more simplification seems to be possible for a general anisotropic medium. In this thesis, the integration domain for regular part is further reduced to a quarter of a sphere for the particular case of transversely isotropic material. This reduction proposed for the first time in this thesis nearly halves the number of integration points for the evaluation of regular part of dynamic Green's function. It significantly reduces the computational time.
25
Bruciaferri, Diego. "Study of a wind-wave numerical model and its integration with ocean and oil-spill numerical models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6757/.
Повний текст джерелаАнотація:
The ability to represent the transport and fate of an oil slick at the sea surface is a formidable task. By using an accurate numerical representation of oil evolution and movement in seawater, the possibility to asses and reduce the oil-spill pollution risk can be greatly improved. The blowing of the wind on the sea surface generates ocean waves, which give rise to transport of pollutants by wave-induced velocities that are known as Stokes’ Drift velocities. The Stokes’ Drift transport associated to a random gravity wave field is a function of the wave Energy Spectra that statistically fully describe it and that can
be provided by a wave numerical model. Therefore, in order to perform an accurate numerical simulation of the oil motion in seawater, a coupling of the oil-spill model with a wave forecasting model is needed. In this Thesis work,
the coupling of the MEDSLIK-II oil-spill numerical model with the SWAN wind-wave numerical model has been performed and tested. In order to improve the knowledge of the wind-wave model and its numerical performances,
a preliminary sensitivity study to different SWAN model configuration has been carried out. The SWAN model results have been compared with the ISPRA directional buoys located at Venezia, Ancona and Monopoli and the best model settings have been detected. Then, high resolution currents provided by a relocatable model (SURF) have been used to force both the wave and the oil-spill models and its coupling with the SWAN model has been tested. The trajectories of four drifters have been simulated by using JONSWAP parametric spectra or SWAN directional-frequency energy output spectra and results have been compared with the real paths traveled by the drifters.
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Honeycutt, Rebecca Lee. "Higher order algorithms for the numerical integration of stochastic differential equations." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/29907.
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Massow, Claire L. S. "Bifurcation and Numerical Integration Analysis of Parametric Excitation of Inclined Cables." Thesis, University of Bristol, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.520591.
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Iragi, Bakulikira. "On the numerical integration of singularly perturbed Volterra integro-differential equations." University of the Western Cape, 2017. http://hdl.handle.net/11394/5669.
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Magister Scientiae - MScEfficient numerical approaches for parameter dependent problems have been an inter- esting subject to numerical analysts and engineers over the past decades. This is due to the prominent role that these problems play in modeling many real life situations in applied sciences. Often, the choice and the e ciency of the approaches depend on the nature of the problem to solve. In this work, we consider the general linear first-order singularly perturbed Volterra integro-differential equations (SPVIDEs). These singularly perturbed problems (SPPs) are governed by integro-differential equations in which the derivative term is multiplied by a small parameter, known as "perturbation parameter". It is known that when this perturbation parameter approaches zero, the solution undergoes fast transitions across narrow regions of the domain (termed boundary or interior layer) thus affecting the convergence of the standard numerical methods. Therefore one often seeks for numerical approaches which preserve stability for all the values of the perturbation parameter, that is "numerical methods. This work seeks to investigate some "numerical methods that have been used to solve SPVIDEs. It also proposes alternative ones. The various numerical methods are composed of a fitted finite difference scheme used along with suitably chosen interpolating quadrature rules. For each method investigated or designed, we analyse its stability and convergence. Finally, numerical computations are carried out on some test examples to con rm the robustness and competitiveness of the proposed methods.
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Dickson, Neil Edwin Matthew. "The integration of multi-scale hydrogeophysical data into numerical groundwater flow models." Thesis, Queen's University Belfast, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.680157.
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Throughout this research, geophysical data is utilised to constrain numerical groundwater flow models at two applied study areas: a sandstone aquifer in Northern Ireland and a basement rock aquifer in Benin, west Africa. In Northern Ireland, airborne passive magnetics data are used to determine regional heterogeneity occurrence combined with methods of upscaling / equivalence and a density function. Furthermore, a stochastic component is undertaken in the form of multiple point statistics. This analysis performs a probability simulation and pattern matching to determine a statistical occurrence of heterogeneity distribution. In Benin, point magnetic resonance sounding data and electrical resistivity tomography surveys are utilised to determine relationships to hydrogeological properties to aid many conceptualisations of the. region. All studies employed finite element groundwater flow modelling, alongside comparative statistics and model ranking to determine the success and applicability of such analysis. In Northern Ireland, the deterministic analysis indicates that an intermediate level of upscaling (between field scale and one regional anisotropy value) provides statistically significant results at regional scale. The stochastic analysis effectively 'cleans' the magnetics data to provide a new distribution of regional heterogeneity. Modelling results are relatively comparable to the deterministic analysis and demonstrate the successful application of continuous geophysical data into model parameterisation. In Benin, all models provide significant results despite variations in model geometry and parameter conceptualisation. Point geophysical data permits effective model creation and parameter distribution through positive correlation to hydro-structural controls. For all models, minimal boundary conditions are applied and no post-processing is performed. As a result, the benefit of adapting geophysics for model parameterisation is clearly evident and suggests new hydrogeological paradigms for the study areas. Further work is required with regard to predicted anthropogenic and climate change scenarios.
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Sharma, Harsh Apurva. "Structure-preserving Numerical Methods for Engineering Applications." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99912.
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This dissertation develops a variety of structure-preserving algorithms for mechanical systems with external forcing and also extends those methods to systems that evolve on non-Euclidean manifolds. The dissertation is focused on numerical schemes derived from variational principles – schemes that are general enough to apply to a large class of engineering problems. A theoretical framework that encapsulates variational integration for mechanical systems with external forcing and time-dependence and which supports the extension of these methods to systems that evolve on non-Euclidean manifolds is developed. An adaptive time step, energy-preserving variational integrator is developed for mechanical systems with external forcing. It is shown that these methods track the change in energy more accurately than their fixed time step counterparts. This approach is also extended to rigid body systems evolving on Lie groups where the resulting algorithms preserve the geometry of the configuration space in addition to being symplectic as well as energy and momentum-preserving. The advantages of structure-preservation in the numerical simulation are illustrated by various representative examples from engineering applications, which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching.Doctor of Philosophy
Accurate numerical simulation of dynamical systems over long time horizons is essential in applications ranging from particle physics to geophysical fluid flow to space hazard analysis. In many of these applications, the governing physical equations derive from a variational principle and their solutions exhibit physically meaningful invariants such as momentum, energy, or vorticity. Unfortunately, most traditional numerical methods do not account for the underlying geometric structure of the physical system, leading to simulation results that may suggest nonphysical behavior. In this dissertation, tools from geometric mechanics and computational methods are used to develop numerical integrators that respect the qualitative features of the physical system. The research presented here focuses on numerical schemes derived from variational principles– schemes that are general enough to apply to a large class of engineering problems. Energy-preserving algorithms are developed for mechanical systems by exploiting the underlying geometric properties. Numerical performance comparisons demonstrate that these algorithms provide almost exact energy preservation and lead to more accurate prediction. The advantages of these methods in the numerical simulation are illustrated by various representative examples from engineering applications, which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching.
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Petri, Cátia. "Relação entre níveis de significância Bayesiano e freqüentista: e-value e p-value em tabelas de contingência." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-14062007-103802/.
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O FBST (Full Bayesian Significance Test) é um procedimento para testar hipóteses precisas, apresentado por Pereira e Stern (1999), e baseado no cálculo da probabilidade posterior do conjunto tangente ao conjunto que define a hipótese nula. Este procedimento é uma alternativa Bayesiana aos testes de significância usuais. Neste trabalho, estudamos a relação entre os resultados do FBST e de um teste freqüentista, o TRVG (Teste da Razão de Verossimilhanças Generalizado), através de alguns problemas clássicos de testes de hipóteses. Apresentamos, também, todos os procedimentos computacionais utilizados para a resolução automática dos dois testes para grandes amostras, necessária ao estudo da relação entre os testes.FBST (Full Bayesian Significance Test) is a procedure to test precise hypotheses, presented by Pereira and Stern (1999), which is based on the calculus of the posterior probability of the set tangent to the set that defines the null hypothesis. This procedure is a Bayesian alternative to the usual significance tests. In the present work we study the relation between the FBST\'s results and those of a frequentist test, GLRT (Generalised Likelihood Ratio Test) through some classical problems in hypotesis testing. We also present all computer procedures that compose the automatic solutions for applying FBST and GLRT on big samples what was necessary for studying the relation between both tests.
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Randall, Rochelle E. "Approximation and integration on compact subsets of Euclidean space by Rochelle Randall." Click here to access thesis, 2008. http://www.georgiasouthern.edu/etd/archive/summer2008/rochelle_e_randall/randall_rochelle_e_200808_ms.pdf.
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Thesis (M.S.)--Georgia Southern University, 2008."A thesis submitted to the Graduate Faculty of Georgia Southern University in partial fulfillment of the requirements for the degree Master of Science." Directed by Steven Damelin. ETD. Includes bibliographical references (p. 41-42)
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NORONHA, MARCOS AURELIO MARQUES. "ADVANCED NUMERICAL INTEGRATION TECHNIQUES AND OBJECT ORIENTED PROGRAMMING APPLIED TO BOUNDARY ELEMENT METHODS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1998. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=2060@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICODEUTSCHER AKADEMISCHER AUSTAUSCHDIENST
Em análises efetuadas através de Métodos de Elementos de Contorno, o procedimento de integração exerce um papel fundamental, já que faz-se necessária a avaliação de integrais singulares e quase-singulares que introduzem erros numéricos nos resultados quando não são devidamente avaliadas. Nos últimos anos, vários pesquisadores sugeriram diferentes técnicas de integração para tratar os problemas de integração de uma forma adequada. Este trabalho inicia apresentando alguns conceitos básicos e uma revisão bibliográfica das principais técnicas sugeridas. Em seguida, apresenta-se uma técnica de integração unificada, que possui uma forma simples e oferece resultados com excelente precisão. A técnica proposta foi aplicada para integrais singulares ou quase- singulares possuindo pólos simples ou múltiplos, sendo que tanto integrais unidimensionais quanto integrais bidimensionais foram consideradas.Paralelamente ao estudo das integrais, foi desenvolvido um programa computacional em linguagem orientada a objetos (C++), destinado a implementar simultaneamente a formulação convencional e as formulações híbridas dos Métodos de Elementos de Contorno. Da forma em que foi planejado, a implementação suporta diferentes aplicações de análises de engenharia. Este programa resultou de um trabalho conjunto realizado com pesquisadores da Universidade de Stuttgart. Por fim, apresentam-se diversos exemplos numéricos e resultados de análises, ressaltando o bom desempenho da técnica proposta e a influência do procedimento de integração em análises através de Métodos de Elementos de Contorno.
In Boundary Element Method analysis, the integration procedure is one of the most important tasks, since one has to deal with singular and quasi-singular integrals which introduce numerical errors in the results, if they are not evaluated adequately. In the last years, several researchers have suggested different techniques with the aim of handling the problem adequately. This work begins presenting some basic concepts and a review of the most important work published before. Following, it introduces a unified integration technique which has a simple form and provides highly accurate results. The proposed scheme also deals with one- or two-dimensional singular or quasi- singular integrals having single or multiple poles. Besides the study of the integrals, a computational code was developed using an objectoriented computer language (C++). This code takes into account the conventional and hybrid formulations of the Boundary Element Method and supports different types of engineering analysis. This computer program was developed in a frame of a joint project with some researchers from the University of Stuttgart.Finally, several numerical examples and analysis results are displayed, showing the good performance of the proposed technique and the influence of the integration task in analysis using Boundary Element Methods.
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Considine, Seamus. "Modified linear multistep methods for the numerical integration of stiff initial value problems." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47005.
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Nazari, Farshid. "Strongly Stable and Accurate Numerical Integration Schemes for Nonlinear Systems in Atmospheric Models." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32128.
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Nonlinearity accompanied with stiffness in atmospheric boundary layer physical parameterizations is a well-known concern in numerical weather prediction (NWP) models. Nonlinear diffusion equations, furthermore, are a class of equations which are extensively applicable in different fields of science and engineering. Numerical stability and accuracy is a common concern in this class of equation.
In the present research, a comprehensive effort has been made toward the temporal integration of such equations. The main goal is to find highly stable and accurate numerical methods which can be used specifically in atmospheric boundary layer simulations in weather and climate prediction models, and extensively in other models where nonlinear differential equations play an important role, such as magnetohydrodynamics and Navier-Stokes equations.
A modified extended backward differentiation formula (ME BDF) scheme is adapted and proposed at the first stage of this research. Various aspects of this scheme, including stability properties, linear stability analysis, and numerical experiments, are studied with regard to applications for the time integration of commonly used nonlinear damping and diffusive systems in atmospheric boundary layer models. A new temporal filter which leads to significant improvement of numerical results is proposed.
Nonlinear damping and diffusion in the turbulent mixing of the atmospheric boundary layer is dealt with in the next stage by using optimally stable singly-diagonally-implicit Runge-Kutta (SDIRK) methods, which have been proved to be effective and computationally efficient for the challenges mentioned in the literature. Numerical analyses are performed, and two schemes are modified to enhance their numerical features and stability.
Three-stage third-order diagonally-implicit Runge-Kutta (DIRK) scheme is introduced by optimizing the error and linear stability analysis for the aforementioned nonlinear diffusive system. The new scheme is stable for a wide range of time steps and is able to resolve different diffusive systems with diagnostic turbulence closures, or prognostic ones with a diagnostic length scale, with enhanced accuracy and stability compared to current schemes. The procedure implemented in this study is quite general and can be used in other diffusive systems as well.
As an extension of this study, high-order low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes are analyzed and introduced, based on the optimization of amplification and phase errors for wave propagation, and various optimized schemes can be obtained. The new scheme shows no dissipation. It is illustrated mathematically and numerically that the new scheme preserves fourth-order accuracy. The numerical applications contain the wave equation with and without a stiff nonlinear source term. This shows that different optimized schemes can be investigated for the solution of systems where physical terms with different behaviours exist.
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Constantinescu, Emil Mihai. "Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/27938.
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Numerical simulation is necessary to understand natural phenomena, make assessments and predictions in various research and engineering fields, develop new technologies, etc. New algorithms are needed to take advantage of the increasing computational resources and utilize the emerging hardware and software infrastructure with maximum efficiency.
Adaptive numerical discretization methods can accommodate problems with various physical, scale, and dynamic features by adjusting the resolution, order, and the type of method used to solve them. In applications that simulate real systems, the numerical accuracy of the solution is typically just one of the challenges. Measurements can be included in the simulation to constrain the numerical solution through a process called data assimilation in order to anchor the simulation in reality.
In this thesis we investigate adaptive discretization methods and data assimilation approaches for large-scale numerical simulations. We develop and investigate novel multirate and implicit-explicit methods that are appropriate for multiscale and multiphysics numerical discretizations. We construct and explore data assimilation approaches for, but not restricted to, atmospheric chemistry applications. A generic approach for describing the structure of the uncertainty in initial conditions that can be applied to the most popular data assimilation approaches is also presented.
We show that adaptive numerical methods can effectively address the discretization of large-scale problems. Data assimilation complements the adaptive numerical methods by correcting the numerical solution with real measurements. Test problems and large-scale numerical experiments validate the theoretical findings. Synergistic approaches that use adaptive numerical methods within a data assimilation framework need to be investigated in the future.Ph. D.
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Roberts, Bryndan. "Integration of an electrical discharge machining module onto a reconfigurable machine tool." Thesis, Nelson Mandela Metropolitan University, 2014. http://hdl.handle.net/10948/6182.
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Electrical Discharge Machining (EDM) is a non-contact manufacturing process in which material is removed from a metal workpiece by high frequency electrical pulses produced between an electrode and the workpiece. EDM machines are usually stand-alone devices, and are quite expensive. The objective of this research was to integrate an EDM machine and an existing reconfigurable CNC machine tool, using a modular approach, to enable conventional milling and EDM to be conducted in a co-ordinated fashion on the same machine tool.
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Sinescu, Vasile. "Construction of lattice rules for multiple integration based on a weighted discrepancy." The University of Waikato, 2008. http://hdl.handle.net/10289/2542.
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High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and chemistry of molecules, statistical mechanics and more recently, in financial applications. In order to approximate multidimensional integrals, one may use Monte Carlo methods in which the quadrature points are generated randomly or quasi-Monte Carlo methods, in which points are generated deterministically. One particular class of quasi-Monte Carlo methods for multivariate integration is represented by lattice rules. Lattice rules constructed throughout this thesis allow good approximations to integrals of functions belonging to certain weighted function spaces. These function spaces were proposed as an explanation as to why integrals in many variables appear to be successfully approximated although the standard theory indicates that the number of quadrature points required for reasonable accuracy would be astronomical because of the large number of variables. The purpose of this thesis is to contribute to theoretical results regarding the construction of lattice rules for multiple integration. We consider both lattice rules for integrals over the unit cube and lattice rules suitable for integrals over Euclidean space. The research reported throughout the thesis is devoted to finding the generating vector required to produce lattice rules that have what is termed a low weighted discrepancy . In simple terms, the discrepancy is a measure of the uniformity of the distribution of the quadrature points or in other settings, a worst-case error. One of the assumptions used in these weighted function spaces is that variables are arranged in the decreasing order of their importance and the assignment of weights in this situation results in so-called product weights . In other applications it is rather the importance of group of variables that matters. This situation is modelled by using function spaces in which the weights are general . In the weighted settings mentioned above, the quality of the lattice rules is assessed by the weighted discrepancy mentioned earlier. Under appropriate conditions on the weights, the lattice rules constructed here produce a convergence rate of the error that ranges from O(n−1/2) to the (believed) optimal O(n−1+δ) for any δ gt 0, with the involved constant independent of the dimension.
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Sæbø, Karsten Krog. "Pricing Exotic Options with the Normal Inverse Gaussian Market Model using Numerical Path Integration." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2009. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9878.
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Thomas, David O. "A numerical investigation of time integration schemes applied to dynamic solution of mooring lines." Thesis, University of Newcastle Upon Tyne, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385283.
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Scott, Roderick Spencer. "Parallel-processor-based Gaussian beam tracer for use in ocean acoustic tomography." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA232420.
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Thesis (M.S. in Engineering Acoustics and M.S. in Electrical Engineering)--Naval Postgraduate School, June 1990.Thesis Advisor(s): Miller, James H. ; Chiu, Ching-Sang ; Yang, Chyan. "June 1990." Description based on title screen as viewed on October 20, 2009. DTIC Identifier(s): Acoustic Tomography, Theses, Range Kutta Fehlberg Method, C Programming Language, Macintosh 2 Computers, Transputers, Parallel Processors, Numerical Integration. Author(s) subject terms: Acoustic Tomography, Ray Tracing, Parallel Processing, Gaussian Beams, Transputers. Includes bibliographical references (p. 122-124). Also available online.
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Kraus, Michal. "Paralelní výpočetní architektury založené na numerické integraci." Doctoral thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2013. http://www.nusl.cz/ntk/nusl-261227.
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This thesis deals with continuous system simulation. The systems can be described by system of differential equations or block diagram. Differential equations are usually solved by numerical methods that are integrated into simulation software such as Matlab, Maple or TKSL. Taylor series method has been used for numerical solutions of differential equations. The presented method has been proved to be both very accurate and fast and also procesed in parallel systems. The aim of the thesis is to design, implement and compare a few versions of the parallel system.
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Kalaver, Satchidanand Anil. "Management of reference frames in simulation and its application to error reduction in numerical integration." Thesis, Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/12406.
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Brunner, Daniel [Verfasser], Florian [Gutachter] Heiß, and Joel [Gutachter] Stiebale. "Numerical Integration in Random Coefficient Models of Demand / Daniel Brunner ; Gutachter: Florian Heiß, Joel Stiebale." Düsseldorf : Universitäts- und Landesbibliothek der Heinrich-Heine-Universität Düsseldorf, 2017. http://d-nb.info/1138114510/34.
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Rigola, Serrano Joaquim. "Numerical simulation and experimental validation of hermetic reciprocating compressors. Integration in vapour compression refrigerating systems." Doctoral thesis, Universitat Politècnica de Catalunya, 2002. http://hdl.handle.net/10803/6684.
Повний текст джерелаАнотація:
The numerical simulation model presented is based on the integration of the fluid conservation equations (continuity, momentum and energy) in the whole compressor domain (compression chamber, valves, manifolds, mufflers, connecting tubes, parallel paths, etc.) using instantaneous local mean values for the different variables. It is interesting to remark how momentum equation has been taken into account in all compressor parts and the possibility to solve parallel paths, resonators, etc. Effective flow areas are evaluated considering multidimensional models based on modal analysis of fluid interaction in the valve. Then, second and third order vibration models of valve are also considered. The possibility to use compound bound has been also implemented.The force balances in the crankshaft connecting rod mechanical system are simultaneously solved at each time-step considered in the thermal and fluid dynamic compressor model. It allows to evaluate the instantaneous compression chamber volume and the different forces in the crankshaft connecting rod mechanical system. Mechanical system forces allows to know important information to predict possible
over-stresses in piston, piston pin, crankshaft, connecting rod, etc.
The thermal analysis of the solid elements is based on global energy balances at each macro volume considered (shell, muffler, tubes, cylinder head, crankcase, motor, etc.). Some improvements can be implemented (shell conduction, heat transfer coefficient evaluation, etc.).
The resulting governing equations (fluid flow, valve dynamics, conduction heat transfer in solids, etc.) are discretized by means of a fully implicit control volume formulation. The complete set of algebraic equations are coupled using the segregated he complete set of algebraic equations are coupled using the segregated pressure based algorithm Semi-Implicit Method for Pressure-Linked Equations(SIMPLEC) extended to compressible flow. Second and third time order schemes have been implemented for the transient terms.
An extensive hermetic reciprocating compressor experimental validation has been presented and the experimental know-how acquired has been highlighted. Furthermore, two commercial hermetic reciprocating compressor have been instrumented in detail to obtain the thermal temperatures map and the pressure fluid evolutions along compressor for different working conditions. It is interesting to remark as a novelty, the use of very small absolute pressure transducers, instead of the standard relative transducers. They allow to know instantaneous absolute pressure inside compressor chamber, without the necessity of measurement an absolute pressure outside the compression chamber (as is usual in this kind of experimental works).
The global comparative results have allowed to check the possibilities of the numerical simulation presented above and its accuracy compared with experimental data. After that, this work show the capabilities offered by the simulation presented and its final objective, a better understanding of the thermal and fluid dynamic compressor behaviour to improve the design of these equipments.
Then, the objective has been to review and present different physically meaningful parameters that characterize the reciprocating compressor behaviour (volumetric efficiency, isentropic efficiency, heat transfer efficiency, mechanical, electrical and heat losses, Coefficient of Performance, etc.), their influence detachment and evolution under different working conditions, with the idea to predict the performance of hermetic reciprocating compressors under different working conditions using the above mentioned non-dimensional parameters.
Finally, a parametric study of hermetic reciprocating compressors behaviour has been carried out. Results presented show the influence of different aspects (geometry, valves, motor, working conditions, etc.) in the compressor behaviour.
The parametric studies and compressor characterization detachment allows also a better implementation of simplest models of the compressors in the thermal and fluid dynamic numerical simulation of vapour compressor cycles together with the rest of elements.
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Khan, Kamran-Ahmed. "A time integration scheme for stress - temperature dependent viscoelastic behaviors of isotropic materials." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1146.
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Mikulka, Jiří. "Numerické výpočty určitých integrálů." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2014. http://www.nusl.cz/ntk/nusl-236141.
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The application of the finite integral of multiple variable functions is penetrating into more and more industries and science disciplines. The demands placed on solutions to these problems (such as high accuracy or high speed) are often quite contradictory. Therefore, it is not always possible to apply analytical approaches to these problems; numerical methods provide a suitable alternative. However, the ever-growing complexity of these problems places too high a demand on many of these numerical methods, and so neither of these methods are useful for solving such problems. The goal of this thesis is to design and implement a new numerical method that provides highly accurate and very fast computation of finite integrals of multiple variable functions. This new method combines pre-existing approaches in the field of numerical mathematics.
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Ngounda, Edgard. "Numerical Laplace transformation methods for integrating linear parabolic partial differential equations." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/2735.
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Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2009.ENGLISH ABSTRACT: In recent years the Laplace inversion method has emerged as a viable alternative method for the numerical solution of PDEs. Effective methods for the numerical inversion are based on the approximation of the Bromwich integral. In this thesis, a numerical study is undertaken to compare the efficiency of the Laplace inversion method with more conventional time integrator methods. Particularly, we consider the method-of-lines based on MATLAB’s ODE15s and the Crank-Nicolson method. Our studies include an introductory chapter on the Laplace inversion method. Then we proceed with spectral methods for the space discretization where we introduce the interpolation polynomial and the concept of a differentiation matrix to approximate derivatives of a function. Next, formulas of the numerical differentiation formulas (NDFs) implemented in ODE15s, as well as the well-known second order Crank-Nicolson method, are derived. In the Laplace method, to compute the Bromwich integral, we use the trapezoidal rule over a hyperbolic contour. Enhancement to the computational efficiency of these methods include the LU as well as the Hessenberg decompositions. In order to compare the three methods, we consider two criteria: The number of linear system solves per unit of accuracy and the CPU time per unit of accuracy. The numerical results demonstrate that the new method, i.e., the Laplace inversion method, is accurate to an exponential order of convergence compared to the linear convergence rate of the ODE15s and the Crank-Nicolson methods. This exponential convergence leads to high accuracy with only a few linear system solves. Similarly, in terms of computational cost, the Laplace inversion method is more efficient than ODE15s and the Crank-Nicolson method as the results show. Finally, we apply with satisfactory results the inversion method to the axial dispersion model and the heat equation in two dimensions.
AFRIKAANSE OPSOMMING: In die afgelope paar jaar het die Laplace omkeringsmetode na vore getree as ’n lewensvatbare alternatiewe metode vir die numeriese oplossing van PDVs. Effektiewe metodes vir die numeriese omkering word gebasseer op die benadering van die Bromwich integraal. In hierdie tesis word ’n numeriese studie onderneem om die effektiwiteit van die Laplace omkeringsmetode te vergelyk met meer konvensionele tydintegrasie metodes. Ons ondersoek spesifiek die metode-van-lyne, gebasseer op MATLAB se ODE15s en die Crank-Nicolson metode. Ons studies sluit in ’n inleidende hoofstuk oor die Laplace omkeringsmetode. Dan gaan ons voort met spektraalmetodes vir die ruimtelike diskretisasie, waar ons die interpolasie polinoom invoer sowel as die konsep van ’n differensiasie-matriks waarmee afgeleides van ’n funksie benader kan word. Daarna word formules vir die numeriese differensiasie formules (NDFs) ingebou in ODE15s herlei, sowel as die welbekende tweede orde Crank-Nicolson metode. Om die Bromwich integraal te benader in die Laplace metode, gebruik ons die trapesiumreël oor ’n hiperboliese kontoer. Die berekeningskoste van al hierdie metodes word verbeter met die LU sowel as die Hessenberg ontbindings. Ten einde die drie metodes te vergelyk beskou ons twee kriteria: Die aantal lineêre stelsels wat moet opgelos word per eenheid van akkuraatheid, en die sentrale prosesseringstyd per eenheid van akkuraatheid. Die numeriese resultate demonstreer dat die nuwe metode, d.i. die Laplace omkeringsmetode, akkuraat is tot ’n eksponensiële orde van konvergensie in vergelyking tot die lineêre konvergensie van ODE15s en die Crank-Nicolson metodes. Die eksponensiële konvergensie lei na hoë akkuraatheid met slegs ’n klein aantal oplossings van die lineêre stelsel. Netso, in terme van berekeningskoste is die Laplace omkeringsmetode meer effektief as ODE15s en die Crank-Nicolson metode. Laastens pas ons die omkeringsmetode toe op die aksiale dispersiemodel sowel as die hittevergelyking in twee dimensies, met bevredigende resultate.
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Khama, Mopeli. "Numerical simulation of bubble columns by integration of bubble cell model into the population balance framework." Master's thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/9118.
Повний текст джерелаАнотація:
Includes bibliographical references.Bubble column reactors are widely used in the chemicals industry including pharmaceuticals, waste water treatment, flotation etc. The reason for their wide application can be attributed to the excellent rates of heat and mass transfer that are achieved between the dispersed and continuous phases in such reactors. Although these types of contactors possess the properties that make them attractive for many applications, there still remain significant challenges pertaining to their design, scale-up and optimization. These challenges are due to the hydrodynamics being complex to simulate. In most cases the current models fail to capture the dynamic features of a multiphase flow. In addition, since most of the developed models are empirical, and thus beyond the operating conditions in which they were developed, their accuracy can no longer be retained. As a result there is a necessity to develop eneric models which can predict hydrodynamics, heat and mass transfer over a wide range of operating conditions. With regard to simulating these systems, Computational Fluid Dynamics (CFD) has been used in various studies to predict mass and heat transfer characteristics, velocity gradients etc (Martín et al., 2009; Guha et al., 2008; Olmos et al., 2001; Sanyal et al., 1999; Sokolichin et al., 1997).The efficient means for solving CFD are needed to allow for investigation of more complex systems. In addition, most models report constant bubble particle size which is a limitation as this can only be applicable in the homogenous flow regime where there is no complex interaction between the continuous and dispersed phase (Krishna et al., 2000; Sokolichin & Eigenberger., 1994). The efficient means for solving CFD intimated above is addressed in the current study by using Bubble Cell Model (BCM). BCM is an algebraic model that predicts velocity, concentration and thermal gradients in the vicinity of a single bubble and is a computationally efficient approach The objective of this study is to integrate the BCM into the Population Balance Model (PBM) framework and thus predict overall mass transfer rate, overall intrinsic heat transfer coefficient, bubble size distribution and overall gas hold-up. The experimental determination of heat transfer coefficient is normally a difficult task, and in the current study the mass transfer results were used to predict heat transfer coefficient by applying the analogy that exists between heat and mass transfer. In applying the analogy, the need to determine the heat transfer coefficient experimentally or numerically was obviated. The findings indicate that at the BCM Renumbers (Max Re= 270), there is less bubble-bubble and eddy-bubble interactions and thus there is no difference between the inlet and final size distributions. However upon increasing Re number to higher values, there is a pronounced difference between the inlet and final size distributions and therefore it is important to extend BCM to higher Re numbers. The integration of BCM into the PBM framework was validated against experimental correlations reported in the literature. In the model validation, the predicted parameters showed a close agreement to the correlations with overall gas hold-up having an error of ±0.6 %, interfacial area ±3.36 % and heat transfer coefficient ±15.4 %. A speed test was also performed to evaluate whether the current model is quicker as compared to other models. Using MATLAB 2011, it took 15.82 seconds for the current model to predict the parameters of interest by integration of BCM into the PBM framework. When using the same grid points in CFD to get the converged numerical solutions for the prediction of mass transfer coefficient, the computational time was found to be 1.46 minutes. It is now possible to predict the intrinsic mass transfer coefficient using this method and the added advantage is that it allows for the decoupling of mass transfer mechanisms, thus allowing for more detailed designs.The decoupling of mass transfer mechanisms in this context refers to the separate determination of the intrinsic mass transfer coefficient and interfacial area.
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Shepherd, David. "Numerical methods for dynamic micromagnetics." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/numerical-methods-for-dynamic-micromagnetics(e8c5549b-7cf7-44af-8191-5244a491d690).html.
Повний текст джерелаАнотація:
Micromagnetics is a continuum mechanics theory of magnetic materials widely used in industry and academia. In this thesis we describe a complete numerical method, with a number of novel components, for the computational solution of dynamic micromagnetic problems by solving the Landau-Lifshitz-Gilbert (LLG) equation. In particular we focus on the use of the implicit midpoint rule (IMR), a time integration scheme which conserves several important properties of the LLG equation. We use the finite element method for spatial discretisation, and use nodal quadrature schemes to retain the conservation properties of IMR despite the weak-form approach. We introduce a novel, generally-applicable adaptive time step selection algorithm for the IMR. The resulting scheme selects error-appropriate time steps for a variety of problems, including the semi-discretised LLG equation. We also show that it retains the conservation properties of the fixed step IMR for the LLG equation. We demonstrate how hybrid FEM/BEM magnetostatic calculations can be coupled to the LLG equation in a monolithic manner. This allows the coupled solver to maintain all properties of the standard time integration scheme, in particular stability properties and the energy conservation property of IMR. We also develop a preconditioned Krylov solver for the coupled system which can efficiently solve the monolithic system provided that an effective preconditioner for the LLG sub-problem is available. Finally we investigate the effect of the spatial discretisation on the comparative effectiveness of implicit and explicit time integration schemes (i.e. the stiffness). We find that explicit methods are more efficient for simple problems, but for the fine spatial discretisations required in a number of more complex cases implicit schemes become orders of magnitude more efficient.