Dissertations / Theses on the topic 'Numerical solutions'
To see the other types of publications on this topic, follow the link: Numerical solutions.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Numerical solutions.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Sundqvist, Per. "Numerical Computations with Fundamental Solutions." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5757.
Full text
2
Briggs, A. J. "Numerical solutions of Hamilton-Jacobi equations." Thesis, University of Sussex, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298668.
Full text
3
Van, Cong Tuan Son. "Numerical solutions to some inverse problems." Diss., Kansas State University, 2017. http://hdl.handle.net/2097/38248.
Full textAbstract:
Doctor of PhilosophyDepartment of Mathematics
Alexander G. Ramm
In this dissertation, the author presents two independent researches on inverse problems: (1) creating materials in which heat propagates a long a line and (2) 3D inverse scattering problem with non-over-determined data. The theories of these methods were developed by Professor Alexander Ramm and are presented in Chapters 1 and 3. The algorithms and numerical results are taken from the papers of Professor Alexander Ramm and the author and are presented in Chapters 2 and 4.
4
Zeineddin, Rafik Paul. "Numerical electromagnetics codes problems, solutions and applications." Ohio : Ohio University, 1993. http://www.ohiolink.edu/etd/view.cgi?ohiou1176315682.
Full text
5
Bratsos, A. G. "Numerical solutions of nonlinear partial differential equations." Thesis, Brunel University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332806.
Full text
6
Iafrati, Alessandro. "Floating body impact : asymptotic and numerical solutions." Thesis, University of East Anglia, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501123.
Full textAbstract:
This thesis is concerned with the estimate of hydrodynamic loads generated during the water entry of bodies, originally floating on a still liquid surface. The analysis assumes the fluid to be ideal and the flow potential. The liquid is treated as incompressible, but the effects of weak compressibility are carefully estimated. A theoretical estimate of the loads in the early stage after the sudden start of the vertical downward motion of the body is derived. The solution is achieved through the method of matched asymptotic expansions, by using the non-dimensional body displacement as a small parameter. A uniformly valid solution is obtained by formulating an inner problem under suitable set of stretched variables and by matching its asymptotic behaviour with the inner limit of the outer solution. The boundary value problem governing the inner solution is strongly nonlinear, with nonlinear boundary conditions imposed on unknown free surface position. The solution is obtained through suitably developed numerical iterative procedures.
7
Tang, Tao. "Numerical solutions of the Navier-Stokes equations." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328961.
Full text
8
Hoang, Nguyen Si. "Numerical solutions to some ill-posed problems." Diss., Kansas State University, 2011. http://hdl.handle.net/2097/9204.
Full textAbstract:
Doctor of PhilosophyDepartment of Mathematics
Alexander G. Ramm
Several methods for a stable solution to the equation $F(u)=f$ have been developed. Here $F:H\to H$ is an operator in a Hilbert space $H$, and we assume that noisy data $f_\delta$, $\|f_\delta-f\|\le \delta$, are given in place of the exact data $f$. When $F$ is a linear bounded operator, two versions of the Dynamical Systems Method (DSM) with stopping rules of Discrepancy Principle type are proposed and justified mathematically. When $F$ is a non-linear monotone operator, various versions of the DSM are studied. A Discrepancy Principle for solving the equation is formulated and justified. Several versions of the DSM for solving the equation are formulated. These methods consist of a Newton-type method, a gradient-type method, and a simple iteration method. A priori and a posteriori choices of stopping rules for these methods are proposed and justified. Convergence of the solutions, obtained by these methods, to the minimal norm solution to the equation $F(u)=f$ is proved. Iterative schemes with a posteriori choices of stopping rule corresponding to the proposed DSM are formulated. Convergence of these iterative schemes to a solution to the equation $F(u)=f$ is proved. This dissertation consists of six chapters which are based on joint papers by the author and his advisor Prof. Alexander G. Ramm. These papers are published in different journals. The first two chapters deal with equations with linear and bounded operators and the last four chapters deal with non-linear equations with monotone operators.
9
D'Alessandro, Valerio. "Numerical solutions of turbulent flows: industrial applications." Doctoral thesis, Università Politecnica delle Marche, 2013. http://hdl.handle.net/11566/242718.
Full textAbstract:
La Computational Fluid-Dynamics (CFD) si trova sempre maggiormente coinvolta nello studio di sistemi energetici innovativi. Quindi è logico pensare a filoni di ricerca in cui si sviluppano metodi numerici efficienti, robusti ed accurati per la soluzione di tali problemi. In questa tesi si affronta la soluzione numerica di alcuni problemi di interesse industriale sia con tecniche risolutive standard che innovative. In particolare sono stati sviluppati solutori ad elavato ordine di accuratezza per flussi incomprimibili basati sul metodo ad elementi finiti discontinui di Galerkin (DG). Il metodo DG è basato su approssimazioni polinomiali all’interno del singolo elemento computazionale senza richiesta di continuità globale della soluzione. Recentemente tale metodo sta ricevendo particolare interesse per l’applicazione a problemi di CFD. Partendo da un codice presistente 2D viscoso, basato su un flusso a comprimibilità artificiale, è stata sviluppata una versione 3D che si sta dimostrando capace di essere utilizata come solutore DNS. Quindi è stato aggiunto il modello di turbolenza di Spalart-Allmaras (SA) sia sulla versione 2D che 3D. Vale la pena notare che la soluzione DG delle equazioni RANS è molto complessa per via dell’enorme rigidezza numerica del problema. In questo lavoro viene proposta un’implementazione innovativa del modello SA che modifica opportunamente i termini sorgenti e diffusivi dell’equazione di evoluzione SA quando la variabile di lavoro, o una delle funzioni di chiusura del modello, diventano negative. E’ importante notare che ad oggi in letteratura non sono presenti lavori che trattano della soluzione DG del sistema di equazioni RANS-SA incomprimibili. L’approccio proposto è stato quindi testato su un’ampia gamma di problemi. Parallelamente è stata studiata sia l’Aerodinamica instazionaria dei rotori eolici di tipo Savonius che il campo di moto interno al tubo vortice ad effetto Ranque-Hilsch (RHVT) attraverso solutori standard a volumi finiti. Nonostante durante questo lavoro di tesi siano stati sviluppati solutori DG per un ampio range di numeri di Reynolds, ad oggi essi non sono stati ancora applicati a problemi come il Savonius o RHVT in quanto al tempo di quelle analisi non si disponeva dei codici allo stato di sviluppo attuale.The study of innovative energy systems often involves complex fluid flows problems and the Computational Fluid Dynamics (CFD) is one of the main tools of analysis. It is very easy to understand as developing new high-accuracy solution techniques for the fluid flow governing equations is of an extreme interesting research area. This work is aimed in the field of numerical solution of turbulent flows problems in industrial configurations with standard and innovative discretization techquines. In this thesis great efforts were addressed in to develop of a high-order Discontinuous Galerkin (DG) solver for incompressible flows in order to enjoy its accuracy in a wide class of industrial problems. DG methods are based on polynomial approximations inside the computational elements with no global continuity requirement and they are receiving an increasing interest in CFD community. features. Starting from a 2D viscous version of a code, based on the artificial compressibility flux DG method [1], in this thesis a 3D version is presented and its suitability for DNS computations is demonstrated. Moreover the Spalart-Allmaras (SA) turbulence model has been implemented in both the 2D and 3D solvers.It is worth noting that DG space discretization of RANS equations is a difficult task due the numerical stiffness of the equations. In this work the SA model is modified in source and diffusion terms to deal with numerical instabilities coming-up when the working variable, or one of the model closure functions, become negative thus unphysical. It is important to remark that in the present literature are not reported others DG solvers for the incompressible RANSSA equations. The realiability, accuracy and robustness of the solution method was assessed computing several test-cases in simple and real-life configurations. Simultaneously unsteady Aerodynamics of the Savonius wind rotor and the flow field inside a Ranque-Hilsch vortex tube (RHVT) were extensively studied with standard finite volume solvers obtaining innovative results. Neverthless in this moment our DG solvers can cover a wide range of Reynolds numbers, they have not still found application to analyze problems as Savonius rotors or RHVT since at the time of those analysis our codes can not deal with that kind of flows.
10
Cuminato, José Alberto. "Numerical solutions of Cauchy integral equations and applications." Thesis, University of Oxford, 1987. http://ora.ox.ac.uk/objects/uuid:434954bb-bf08-448b-9e02-9948d1287e37.
Full textAbstract:
This thesis investigates the polynomial collocation method for the numerical solution of Cauchy type integral equations and the use of those equations and the related numerical techniques to solve two practical problem in Acoustics and Aerodynamics. Chapters I and II include the basic background material required for the development of the main body of the thesis. Chapter I discusses a number of practical problems which can be modelled as a singular integral equations. In Chapter II the theory of those equations is given in great detail. In Chapter III the polynomial collocation method for singular integral equations with constant coefficients is presented. A particular set of collocation points, namely the zeros of the first kind Chebyshev polynomials, is shown to give uniform convergence of the numerical approximation for the cases of the index K = 0. 1. The convergence rate for this method is also given. All these results were obtained under slightly stronger assumptions than the minimum required for the existence of an exact solution. Chapter IV contains a generalization of the results in Chapter III to the case of variable coefficients. In Chapter V an example of a practical problem which results in a singular integral equation and which is successfully solved by the collocation method is described in substantial detail. This problem consists of the interaction of a sound wave with an elastic plate freely suspended in a fluid. It can be modelled by a system of two coupled boundary value problems - the Helmholtz equation and the beam equation. The collocation method is then compared with asymptotic results and a quadrature method due to Miller. In Chapter VI an efficient numerical method is developed for solving problems with discontinuous right-hand sides. Numerical comparison with other methods and possible extensions are also discussed.
11
Postell, Floyd Vince. "High order finite difference methods." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/28876.
Full text
12
Li, Ming. "Numerical solutions for the incompressible Navier-Stokes equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0016/NQ37725.pdf.
Full text
13
Tang, Wei. "Numerical solutions of unsteady flow past rotor sections." Diss., Georgia Institute of Technology, 1986. http://hdl.handle.net/1853/13336.
Full text
14
KURKA, PAULO ROBERTO GARDEL. "NUMERICAL SOLUTIONS FOR EIGENPROBLEMS ASSOCIATED TO SYMMETRIC OPERATORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1985. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=20274@1.
Full textAbstract:
Desenvolve-se uma técnica para a extração de auto-pares relacionados com a solução de problemas de Elementos Finitos. O algoritmo consiste no uso dos métodos da Iteração Inversa e Gradiente Conjugado para a obtenção do vetor solução associado ao menor auto-valor. As soluções do auto-sistema são calculadas sequencialmente pela modificação da matriz dos coeficientes das equações de equilíbrio do problema através do uso de uma técnica de Deflação. O uso extensivo desta técnica introduz auto-valores múltiplos na matriz dos coeficientes, tornando necessário proceder-se a uma combinação dos dois métodos. É efetuado também um estudo para encontrar vetores iniciais apropriados a serem utilizados pelos métodos. O algoritmo foi implementado e alguns resultados de resolução de exemplos são apresentados, para ilustrar o seu desempenho.A vector iterative technique is developed for the extraction of eigenpairs related to the solution of finite element problems. The algorithm consists of using inverse iteration and conjugate gradient methods so as to obtain the solution vector associated to the smallest eigenvalue. Eigensolutions are sequentially calculated by replacing the coefficient matrix in the problem equilibrium equation using a deflation technique. The extensive usage of this technique, introduces multiple eigenvalue in the coefficient matrix, requiring a procedure to combine both methods. Also, a study is performed to find the appropriate starting vector to be used with methods. The algorithm has been implemented and the results of some example solutions are given that yield insight into its predictive capabilities.
15
Simmel, Martin. "Two numerical solutions for the stochastic collection equation." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-215378.
Full textAbstract:
Two different methods are used to solve the stochastic collection equation (SCE) numerically. They are called linear discrete method (LDM) and bin shift method (BSM), respectively. Conceptually, both of them are similar to the well-known discrete method (DM) of Kovetz and Olund. For LDM and BSM, their concept is extended to two prognostic moments. Therefore, the \"splitting factors\" (which are constant in time for DM) become time-dependent for LDM and BSM. Simulations are shown for the Golovin kernel (for which an analytical solution is available) and the hydrodynamic kernel after Hall. Different bin resolutions and time steps are investigated. As expected, the results become better with increasing bin resolution. LDM and BSM do not show the anomalous dispersion which is a weakness of DMEs werden zwei verschiedene Methoden zur numerischen Lösung der \"Gleichung für stochastisches Einsammeln\" (stochastic collection equation, SCE) vorgestellt. Sie werden als Lineare Diskrete Methode (LDM) bzw. Bin Shift Methode (BSM) bezeichnet. Konzeptuell sind beide der bekannten Diskreten Methode (DM) von Kovetz und Olund ähnlich. Für LDM und BSM wird deren Konzept auf zwei prognostische Momente erweitert. Für LDM und BSM werden die\" Aufteil-Faktoren\" (die für DM zeitlich konstant sind) dadurch zeitabhängig. Es werden Simulationsrechnungen für die Koaleszenzfunktion nach Golovin (für die eine analytische Lösung existiert) und die hydrodynamische Koaleszenzfunktion nach Hall gezeigt. Verschiedene Klassenauflösungen und Zeitschritte werden untersucht. Wie erwartet werden die Ergebnisse mit zunehmender Auflösung besser. LDM und BSM zeigen nicht die anomale Dispersion, die eine Schwäche der DM ist
16
Simmel, Martin. "Two numerical solutions for the stochastic collection equation." Wissenschaftliche Mitteilungen des Leipziger Instituts für Meteorologie ; 17 = Meteorologische Arbeiten aus Leipzig ; 5 (2000), S. 61-73, 2000. https://ul.qucosa.de/id/qucosa%3A15149.
Full textAbstract:
Two different methods are used to solve the stochastic collection equation (SCE) numerically. They are called linear discrete method (LDM) and bin shift method (BSM), respectively. Conceptually, both of them are similar to the well-known discrete method (DM) of Kovetz and Olund. For LDM and BSM, their concept is extended to two prognostic
moments. Therefore, the \"splitting factors\" (which are constant in time for DM) become time-dependent for LDM and BSM. Simulations are shown for the Golovin kernel (for which an analytical solution is available) and the hydrodynamic kernel after Hall. Different bin resolutions and time steps are investigated. As expected, the results become better with increasing bin resolution. LDM and BSM do not show the anomalous dispersion which is a weakness of DM.Es werden zwei verschiedene Methoden zur numerischen Lösung der \"Gleichung für stochastisches Einsammeln\" (stochastic collection equation, SCE) vorgestellt. Sie werden als Lineare Diskrete Methode (LDM) bzw. Bin Shift Methode (BSM) bezeichnet. Konzeptuell sind beide der bekannten Diskreten Methode (DM) von Kovetz und Olund ähnlich. Für LDM und BSM wird deren Konzept auf zwei prognostische Momente erweitert. Für LDM und BSM werden die\" Aufteil-Faktoren\" (die für DM zeitlich konstant sind) dadurch zeitabhängig. Es werden Simulationsrechnungen für die Koaleszenzfunktion nach Golovin (für die eine analytische Lösung existiert) und die hydrodynamische Koaleszenzfunktion nach Hall gezeigt. Verschiedene Klassenauflösungen und Zeitschritte werden untersucht. Wie erwartet werden die Ergebnisse mit zunehmender Auflösung besser. LDM und BSM zeigen nicht die anomale Dispersion, die eine Schwäche der DM ist.
17
Lehn, Michael Christian. "FLENS - A Flexible Library for Efficient Numerical Solutions." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:289-vts-64199.
Full text
18
Acosta, Antonio Ramon. "Existence of traveling waves and applications." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/28677.
Full text
19
Keeve, Michael Octavis. "Study and implementation of Gauss Runge-Kutta schemes and application to Riccati equations." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/30956.
Full text
20
蕭偉泉 and Wai-chuen Siu. "Small prime solutions of some ternary equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B31213595.
Full text
21
He, Chuan. "Numerical solutions of differential equations on FPGA-enhanced computers." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1248.
Full text
22
Petrov, Dmitri. "Novel approaches to numerical solutions of quantum field theories /." View online version; access limited to Brown University users, 2005. http://wwwlib.umi.com/dissertations/fullcit/3174659.
Full text
23
Jakobsen, Espen Robstad. "On the theory and numerical analysis of viscosity solutions." Doctoral thesis, Norwegian University of Science and Technology, Norwegian University of Science and Technology, 2001. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-556.
Full text
24
Zhang, Ying Ying. "Numerical solutions for Reflected Stochastic Differential Equations in R+." Thesis, University of Macau, 2007. http://umaclib3.umac.mo/record=b1687708.
Full text
25
Kaya, Yasemin. "Analytical And Numerical Solutions To Rotating Orthotropic Disk Problems." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608868/index.pdf.
Full textAbstract:
Analytical and numerical models are developed to investigate the effect of orthotropy on the stress distribution in variable thickness solid and annular rotating disks. The plastic treatment is based on Hill&rsquos quadratic yield criterion, total deformation theory, and Swift&rsquo
s hardening law. The elastic-plastic stress distributions, residual stresses and radial displacement distributions are obtained after having analysed the cases of rotating solid disk, annular disk with rigid inclusion, annular disk subjected to either internal or external pressure. Thermal loading is also considered for the annular disk with rigid inclusion. Effects of different values of elastic and plastic orthotropy parameters are investigated. It is observed that the elastic orthotropy significantly affects the residual stresses in disks. The most remarkable effect of the plastic orthotropy is observed on the disk with rigid inclusion.
26
Fusco, Amintore. "Continuum mechanics and finite element numerical solutions in geotechnique." Thesis, University of Ottawa (Canada), 1985. http://hdl.handle.net/10393/4571.
Full text
27
Gyurko, Lajos Gergely. "Numerical methods for approximating solutions to rough differential equations." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:d977be17-76c6-46d6-8691-6d3b7bd51f7a.
Full textAbstract:
The main motivation behind writing this thesis was to construct numerical methods to approximate solutions to differential equations driven by rough paths, where the solution is considered in the rough path-sense. Rough paths of inhomogeneous degree of smoothness as driving noise are considered. We also aimed to find applications of these numerical methods to stochastic differential equations. After sketching the core ideas of the Rough Paths Theory in Chapter 1, the versions of the core theorems corresponding to the inhomogeneous degree of smoothness case are stated and proved in Chapter 2 along with some auxiliary claims on the continuity of the solution in a certain sense, including an RDE-version of Gronwall's lemma. In Chapter 3, numerical schemes for approximating solutions to differential equations driven by rough paths of inhomogeneous degree of smoothness are constructed. We start with setting up some principles of approximations. Then a general class of local approximations is introduced. This class is used to construct global approximations by pasting together the local ones. A general sufficient condition on the local approximations implying global convergence is given and proved. The next step is to construct particular local approximations in finite dimensions based on solutions to ordinary differential equations derived locally and satisfying the sufficient condition for global convergence. These local approximations require strong conditions on the one-form defining the rough differential equation. Finally, we show that when the local ODE-based schemes are applied in combination with rough polynomial approximations, the conditions on the one-form can be weakened. In Chapter 4, the results of Gyurko & Lyons (2010) on path-wise approximation of solutions to stochastic differential equations are recalled and extended to the truncated signature level of the solution. Furthermore, some practical considerations related to the implementation of high order schemes are described. The effectiveness of the derived schemes is demonstrated on numerical examples. In Chapter 5, the background theory of the Kusuoka-Lyons-Victoir (KLV) family of weak approximations is recalled and linked to the results of Chapter 4. We highlight how the different versions of the KLV family are related. Finally, a numerical evaluation of the autonomous ODE-based versions of the family is carried out, focusing on SDEs in dimensions up to 4, using cubature formulas of different degrees and several high order numerical ODE solvers. We demonstrate the effectiveness and the occasional non-effectiveness of the numerical approximations in cases when the KLV family is used in its original version and also when used in combination with partial sampling methods (Monte-Carlo, TBBA) and Romberg extrapolation.
28
MA, XIANG. "NUMERICAL SOLUTIONS FOR DIRECT AND INDIRECT (DESIGN) TURBOMACHINERY PROBLEMS." University of Cincinnati / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1146077765.
Full text
29
Yoon, Sung Joon. "Numerical Navier-Stokes solutions of supersonic slot injection problems." Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/54473.
Full textAbstract:
Supersonic slot injection problems were studied by a finite volume method. The numerical technique used is the upwind method of Roe’s flux difference splitting (FDS) with vertical line Gauss-Seidel relaxation applied to the thin layer Navier-Stokes equations. To test the accuracy of the numerical methods without the complications and uncertainties of turbulence modeling, two sample cases were chosen with laminar flows. The sample problems were the compressible laminar boundary layer flow over a flat plate and the laminar boundary layer - shock interaction problem. For these problems, both the results from Roe’s FDS and van Leer’s flux vector splitting (FVS) are compared with exact solutions and experimental data. For the sample problems, comparisons showed that Roe’s FDS method is more accurate than van Leer’s FVS method. Because of the very complicated wave patterns and strong viscous-inviscid interaction produced by supersonic slot injection, an adaptive grid based on the equidistribution law was combined with the solution algorithm. The results from Roe’s FDS method with the adaptive grid showed good results for the supersonic slot injection over a flat plate. For the slot injection over a 10-degree wedge surface case, there is a significant difference between the numerical and experimental wall pressure distribution. Some potential reasons for the discrepancy including 3D effects and/or transition in the reattachment region in the experiments and possibly a need for a much finer grid in the calculations are discussed.Ph. D.
30
Chiang, Shihchung. "Numerical solutions for a class of singular integrodifferential equations." Diss., This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-06062008-151231/.
Full text
31
Luo, Yi. "Numerical Solutions for Stochastic Differential Equations and Some Examples." Diss., CLICK HERE for online access, 2009. http://contentdm.lib.byu.edu/ETD/image/etd2998.pdf.
Full text
32
Lewis, Andrew. "Parallel Optimisation Algorithms for Continuous, Non-Linear Numerical solutions." Thesis, Griffith University, 2004. http://hdl.handle.net/10072/367382.
Full textAbstract:
In computational science and engineering there are growing numbers of increasingly sophisticated, rigorous and realistic numerical simulations of physical systems. Detailed knowledge of a particular area of enquiry is expressed in mathematical terms, realised in computer programs and run on increasingly powerful computer systems. The use of such simulations is now commonplace in a growing collection of industrial design areas. Often, users of these models want to understand their behaviour in response to a variety of input stimuli, bounded by various operational parameters. Commonplace in the engineering design process is the need to find the combination of design parameters that minimise (or maximise) some design objective. Optimisation programs seek to apply mathematical techniques and heuristics to guide a computer in choosing trial parameter sets itself in an attempt to satisfy the expressed design objective.
The more realistic the numerical simulations become, the more demanding of computational resources they become. Many of them consume hours, or days, of computing time on supercomputers to deliver a single trial solution. Optimisation algorithms invariably require the model be run more than once, often many times. In the absence of any means to reduce the computational cost of a single run any further, there can be two responses to this dilemma: 1. reduce the number of model evaluations required by the optimisation algorithm, or 2. reduce the time the whole collection of model evaluations takes by running as many as possible at the same time. The research in this thesis is directed toward developing methods that use the approach of parallel computing to reduce total optimisation time by exploiting concurrency within the optimisation algorithms developed. For generality it assumes the numerical simulations to which it may be applied will have real-valued parameters, i.e. they are continuous, and that they may be non-linear in nature. The following contributions are described: 1. The idea of developing a set of 'sandbox' case studies for effective testing of optimisation algorithms is presented and established as a feasible alternative to the use of artificial test functions. An initial set of problems with varying characteristics is also presented. 2. A parallel implementation of the quasi-Newton gradient method with BFGS update and its efficacy in comparison to a corresponding sequential algorithm and widely-used method of simulated annealing is demonstrated. 3. The use of a method of parallel line search with the Nelder-Mead simplex algorithm and its advantages compared to the original algorithm, in speed and reliability, are clearly shown. 4. New direct search methods, the Reducing Set Concurrent Simplex (RSCS) algorithm with line searching variants, are presented, and their superior performance compared to a variety of direct search methods demonstrated. 5. A novel Evolutionary Programming algorithm using concepts of self-organised criticality, EPSOC, is presented, and demonstrated to be superior in performance to a wide variety of gradient, direct search and stochastic methods on a set of test cases drawn from real-world problems. Evidence is presented of its potential for multi-objective optimisation using a novel implementation with multiple, 'virtual' archives. 6. Methods of preconditioning optimisation problems to reduce the total time taken to achieve an optimal result are presented. Temporal preconditioning, based on the time behaviour of the numerical simulations, is demonstrated to yield substantial speedup. 7. Some conclusions have been drawn on the applicability of specific optimisation methods to different classes of real-world problems. All of the methods described are implemented in the framework of a general-purpose optimisation toolset, Nimrod/O, to provide a sound basis for future work, easy adoption across a wide range of engineering design problems and potential commercial application.Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Computing and Information Technology
Full Text
33
Huang, Jeffrey. "Numerical solutions of continuous wave beam in nonlinear media." PDXScholar, 1987. https://pdxscholar.library.pdx.edu/open_access_etds/3742.
Full textAbstract:
Deformation of a Gaussian beam is observed when it propagates through a plasma. Self-focusing of the beam may be observed when the intensity of the laser increases the index of refraction of plasma gas.
Due to the difficulties in solving the nonlinear partial differential equation in Maxwell's wave equation, a numerical technique has been developed in favor of the traditional analytical method. Result of numerical solution shows consistency with the analytical method. This further suggests the validity of the numerical technique employed.
A three dimensional graphics package was used to depict the numerical data obtained from the calculation. Plots from the data further show the deformation of the Gaussian beam as it propagates through the plasma gas.
34
Murali, Vasanth Kumar. "Code verification using the method of manufactured solutions." Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-11112002-121649.
Full text
35
Lee, Wei R. "Computational studies of some static and dynamic optimisation problems." Thesis, Curtin University, 1999. http://hdl.handle.net/20.500.11937/1492.
Full textAbstract:
In this thesis we shall investigate the numerical solutions to several important practical static and dynamic optimization problems in engineering and physics. The thesis is organized as follows.In Chapter 1 a general literature review is presented, including motivation and development of the problems, and existing results. Furthermore, some existing computational methods for optimal control problems are also discussed.In Chapter 2 the design of a semiconductor device is posed as an optimization problem: given an ideal voltage-current (V - I) characteristic, find one or more physical and geometrical parameters so that the V-I characteristic of the device matches the ideal one optimally with respect to a prescribed performance criterion. The voltage-current characteristic of a semiconductor device is governed by a set of nonlinear partial differential equations (PDE), and thus a black-box approach is taken for the numerical solution to the PDEs. Various existing numerical methods are proposed for the solution of the nonlinear optimization problem. The Jacobian of the cost function is ill-conditioned and a scaling technique is thus proposed to stabilize the resulting linear system. Numerical experiments, performed to show the usefulness of this approach, demonstrate that the approach always gives optimal or near-optimal solutions to the test problems in both two and three dimensions.In Chapter 3 we propose an efficient approach to numerical integration in one and two dimensions, where a grid set with a fixed number of vertices is to be chosen so that the error between the numerical integral and the exact integral is minimized. For one dimensional problem two schemes are developed for sufficiently smooth functions based on the mid-point rectangular quadrature rule and the trapezoidal rule respectively, and another method is also developed for integrands which are not sufficiently smooth. For two dimensional problems two schemes are first developed for sufficiently smooth functions. One is based on the barycenter rule on a rectangular partition, while the other is on a triangular partition. A scheme for insufficiently smooth functions is also developed. For illustration, several examples are solved using the proposed schemes, and the numerical results show the effectiveness of the approach.Chapter 4 deals with optimal recharge and driving plans for a battery-powered electric vehicle. A major problem facing battery-powered electric vehicles is in their batteries: weight and charge capacity. Thus a battery-powered electric vehicle only has a short driving range. To travel for a longer distance, the batteries are required to be recharged frequently. In this chapter we construct a model for a battery-powered electric vehicle, in which driving strategy is to be obtained so that the total traveling time between two locations is minimized. The problem is formulated as an unconventional optimization problem. However, by using the control parameterization enhancing transformation (CPET) (see [100]) it is shown that this unconventional optimization is equivalent to a conventional optimal parameter selection problem. Numerical examples are solved using the proposed method.In Chapter 5 we consider the numerical solution to a class of optimal control problems involving variable time points in their cost functions. The CPET is first used to convert the optimal control problem with variable time points into an equivalent optimal control problem with fixed multiple characteristic times (MCT). Using the control parameterization technique, the time horizon is partitioned into several subintervals. Let the partition points also be taken as decision variables. The control functions are approximated by piecewise constant or piecewise linear functions in accordance with these variable partition points. We thus obtain a finite dimensional optimization problem. The CPET transform is again used to convert approximate optimal control problems with variable partition points into equivalent standard optimal control problems with MCT, where the control functions are piecewise constant or piecewise linear functions with pre-fixed partition points. The transformed problems are essentially optimal parameter selection problems with MCT. The gradient formulae are obtained for the objective function as well as the constraint functions with respect to relevant decision variables. Numerical examples are solved using the proposed method.A numerical approach is proposed in Chapter 6 for constructing an approximate optimal feedback control law of a class of nonlinear optimal control problems. In this approach, the state space is partitioned into subdivisions, and the controllers are approximated by a linear combination of the 3rd order B-spline basis functions. Furthermore, the partition points are also taken as decision variables in this formulation. To show the effectiveness of the proposed approach, a two dimensional and a three dimensional examples are solved by the approach. The numerical results demonstrate that the method is superior to the existing methods with fixed partition points.
36
Hu, Guanghui. "Numerical simulations of the steady Euler equations on unstructured grids." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1106.
Full text
37
Chan, Kwok Cheung. "Shooting method for singularly perturbed two-point boundary value problems." HKBU Institutional Repository, 1998. http://repository.hkbu.edu.hk/etd_ra/274.
Full text
38
Jensen, Max. "Discontinuous Galerkin methods for Friedrichs systems with irregular solutions." Thesis, University of Oxford, 2005. http://sro.sussex.ac.uk/45497/.
Full textAbstract:
This work is concerned with the numerical solution of Friedrichs systems by discontinuous Galerkin finite element methods (DGFEMs). Friedrichs systems are boundary value problems with symmetric, positive, linear first-order partial differential operators and allow the unified treatment of a wide range of elliptic, parabolic, hyperbolic and mixed-type equations. We do not assume that the exact solution of a Friedrichs system belongs to a Sobolev space, but only require that it is contained in the associated graph space, which amounts to differentiability in the characteristic direction. We show that the numerical approximations to the solution of a Friedrichs system by the DGFEM converge in the energy norm under hierarchical h- and p- refinement. We introduce a new compatibility condition for the boundary data, from which we can deduce, for instance, the validity of the integration-by-parts formula. Consequently, we can admit domains with corners and allow changes of the inertial type of the boundary, which corresponds in special cases to the componentwise transition from in- to outflow boundaries. To establish the convergence result we consider in equal parts the theory of graph spaces, Friedrichs systems and DGFEMs. Based on the density of smooth functions in graph spaces over Lipschitz domains, we study trace and extension operators and also investigate the eigensystem associated with the differential operator. We pay particular attention to regularity properties of the traces, that limit the applicability of energy integral methods, which are the theoretical underpinning of Friedrichs systems. We provide a general framework for Friedrichs systems which incorporates a wide range of singular boundary conditions. Assuming the aforementioned compatibility condition we deduce well-posedness of admissible Friedrichs systems and the stability of the DGFEM. In a separate study we prove hp-optimality of least-squares stabilised DGFEMs.
39
Bilodeau, Bernard. "Accuracy of a truncated barotropic spectral model : numerical versus analytical solutions." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66037.
Full text
40
張勁光 and King-kwong Cheung. "Prime solutions in arithmetic progressions of some linear ternary equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B42575874.
Full text
41
LIANG, SHEN-MIN. "REFINED NUMERICAL SOLUTIONS OF THE TRANSONIC FLOW PAST A WEDGE (OBLIQUE SHOCK)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/187911.
Full textAbstract:
An adaptive refinement procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by inclusion of approximated truncation error computed from local subgrid refinement. Following this procedure, a reliable scheme has been developed for refined computations of the flow past a wedge at transonic speeds. Effects of the truncation error on the pressure, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and the wave drag due to the shocks, the existence of a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.
42
Davidsen, Stein-Olav Hagen. "Nonlinear integro-differential Equations : Numerical Solutions by using Spectral Methods." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-22682.
Full textAbstract:
This article deals with numerical solutions of nonlinear integro-differential convection-diffusion equations using spectral methods. More specifically, the spectral vanishing viscosity method is introduced and analyzed to show that its family of numerical solutions is compact, and that its solutions converge to the vanishing viscosity solutions. The method is implemented in code, and numerical results including qualitative plots and convergence estimates are given. The article concludes with a discussion of some important implementation concerns and recommendations for further work related to the topic.
43
Goodson, Troy D. "Numerical solutions to optimal low- and medium-thrust orbit transfers." Thesis, Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/13393.
Full text
44
Yevik, Andrei. "Numerical approximations to the stationary solutions of stochastic differential equations." Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/7777.
Full textAbstract:
This thesis investigates the possibility of approximating stationary solutions of stochastic differential equations using numerical methods. We consider a particular class of stochastic differential equations, which are known to generate random dynamical systems. The existence of stochastic stationary solution is proved using global attractor approach. Euler's numerical method, applied to the stochastic differential equation, is proved to generate a discrete random dynamical system. The existence of stationary solution is proved again using global attractor approach. At last we prove that the approximate stationary point converges in mean-square sense to the exact one as the time step of the numerical scheme diminishes.
45
Beaven, F. "Numerical solutions of the Navier-Stokes equations on generalised grids." Thesis, Swansea University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636065.
Full textAbstract:
This thesis presents a numerical procedure for the solution of compressible laminar viscous flow in two and three dimensions. The scheme is based on the finite volume method due to Jameson for the solution of the compressible Euler equations on triangular meshes. The method has been extended for the solution of flows on generalised structured and unstructured grids. Three flow solvers have been written, a 2-D cell centre code, a 2-D cell vertex code and a 3-D cell centre code. Particular attention has been paid to the discretization of the viscous fluxes and the artificial dissipation terms. A contour integral method is used for the calculation of variable gradients. A number of different stencils for such a calculation are presented and discussed. A finite volume type discretization, due to Natakusumah, has been implemented in the 2-D cell centre code and has been extended to 3-D. A finite element type discretization, due to Jameson, has been implemented in the cell vertex code. Two methods are presented for the calculation of artificial dissipation. An edge differencing method due to Jameson, with additional scaling terms for application to viscous solutions, is presented and is shown to work well provided the mesh is smoothly varying. An alternative contour integral method is shown to produce superior results on unsmooth meshes. Finally, some examples are presented which demonstrate the flexibility of the methods discussed, in particular is the ability to obtain accurate solutions on a large variety of grid types.
46
"Numerical solution of integral equation of the second kind." 1998. http://library.cuhk.edu.hk/record=b5889614.
Full textAbstract:
by Chi-Fai Chan.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.
Includes bibliographical references (leaves 53-54).
Abstract also in Chinese.
Chapter Chapter 1 --- INTRODUCTION --- p.1
Chapter §1.1 --- Polynomial Interpolation --- p.1
Chapter §1.2 --- Conjugate Gradient Type Methods --- p.6
Chapter §1.3 --- Outline of the Thesis --- p.10
Chapter Chapter 2 --- INTEGRAL EQUATIONS --- p.11
Chapter §2.1 --- Integral Equations --- p.11
Chapter §2.2 --- Numerical Treatments of Second Kind Integral Equations --- p.15
Chapter Chapter 3 --- FAST ALGORITHM FOR SECOND KIND INTEGRAL EQUATIONS --- p.20
Chapter §3.1 --- Introduction --- p.20
Chapter §3.2 --- The Approximation --- p.24
Chapter §3.3 --- Error Analysis --- p.35
Chapter §3.4 --- Numerical Examples --- p.40
Chapter §3.5 --- Concluding Remarks --- p.51
References --- p.53
47
Schuster, Markus. "Computation of the stresses on a rigid body in exterior stokes and oseen flows." Thesis, 1998. http://hdl.handle.net/1957/33743.
Full textAbstract:
This paper is about the computation of the stresses on a rigid body from a knowledge
of the far field velocities in exterior Stokes and Oseen flows. The surface of the
body is assumed to be bounded and smooth, and the body is assumed to move with
constant velocity. We give fundamental solutions and derive boundary integral equations
for the stresses. As it turns out, these integral equations are singular, and their
null space is spanned by the normal to the body. We then discretize the problem by
replacing the body by an approximating polyhedron with triangular faces. Using a
collocation method, each integral equation delivers a linear system. Since its matrix
approximates a singular integral operator, the matrix is ill-conditioned, and the solution
is unstable. However, since we know that the problem is uniquely solvable in
the hyperspace orthogonal to the normal, we use regularization methods to get stable
solutions and project them in the normal direction onto the hyperspace.Graduation date: 1999
48
Lee, Chuan-En, and 李傳恩. "numerical solutions of doubly curved laminated shells." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/44467383751198522368.
Full text
49
Carstairs, Alexander. "Numerical Solutions to Two-Dimensional Integration Problems." 2015. http://scholarworks.gsu.edu/math_theses/151.
Full textAbstract:
This paper presents numerical solutions to integration problems with bivariate integrands. Using equally spaced nodes in Adaptive Simpson's Rule as a base case, two ways of sampling the domain over which the integration will take place are examined. Drawing from Ouellette and Fiume, Voronoi sampling is used along both axes of integration and the corresponding points are used as nodes in an unequally spaced degree two Newton-Cotes method. Then the domain of integration is triangulated and used in the Triangular Prism Rules discussed by Limaye. Finally, both of these techniques are tested by running simulations over heavily oscillatory and monomial (up to degree five) functions over polygonal regions.
50
Han, Ruei-Jung, and 韓瑞忠. "Numerical solutions of modulated Taylor vortex flow." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/38777088441130498780.
Full text