Dissertations / Theses on the topic 'Numerical methods'
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Kleditzsch, Stefan, and Birgit Awiszus. "Modeling of Cylindrical Flow Forming Processes with Numerical and Elementary Methods." Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-97124.
Full textMunro, Peter Robert Thomas. "Application of numerical methods to high numerical aperture imaging." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427816.
Full textHilden, Sindre Kristensen. "Numerical Methods for Nonholonomic Mechanics." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2009. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9895.
Full textWe discuss nonholonomic systems in general and numerical methods for solving them. Two different approaches for obtaining numerical methods are considered; discretization of the Lagrange-d'Alembert equations on the one hand, and using the discrete Lagrange-d'Alembert principle to obtain nonholonomic integrators on the other. Among methods using the first approach, we focus on the super partitioned additive Runge-Kutta (SPARK) methods. Among nonholonomic integrators, we focus on a reversible second order method by McLachlan and Perlmutter. Through several numerical experiments the methods we present are compared by considering error-growth, conservation of energy, geometric properties of the solution and how well the constraints are satisfied. Of special interest is the comparison of the 2-stage SPARK Lobatto IIIA-B method and the nonholonomic integrator by McLachlan and Perlmutter, which both are reversible and of second order. We observe a clear connection between energy-conservation and the geometric properties of the numerical solution. To preserve energy in long-time integrations is seen to be important in order to get solutions with the correct qualitative properties. Our results indicate that the nonholonomic integrator by McLachlan and Perlmutter sometimes conserves energy better than the 2-stage SPARK Lobatto IIIA-B method. In a recent work by Jay, however, the same two methods are compared and are found to conserve energy equally well in long-time integrations.
Johansson, Christer. "Numerical methods for waveguide modeling /." Stockholm : Numerical Analysis and Computing Science (NADA), Stockholm university, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-992.
Full textKnight, Katherine. "Numerical methods for vortical flows." Thesis, Cranfield University, 2007. http://hdl.handle.net/1826/4535.
Full textHall, Stuart James. "Numerical methods and Riemannian geometry." Thesis, Imperial College London, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.538692.
Full textAshi, Hala. "Numerical methods for stiff systems." Thesis, University of Nottingham, 2008. http://eprints.nottingham.ac.uk/10663/.
Full textHandschuh, Stefan. "Numerical methods in Tensor Networks." Doctoral thesis, Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-159672.
Full textMöller, Ole. "Numerical methods for gravitational lensing." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620929.
Full textLarsson, Johan, and Isak Ågren. "Numerical Methods for Spectral Clustering." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-275701.
Full textShepherd, 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.
Full textHuang, Yumei. "Numerical methods for image restoration." HKBU Institutional Repository, 2008. http://repository.hkbu.edu.hk/etd_ra/908.
Full textDokuchaev, Mikhail. "Numerical Methods for Option Pricing." Thesis, Curtin University, 2021. http://hdl.handle.net/20.500.11937/86211.
Full textDENICH, ELEONORA. "Numerical methods for electromagnetic inversion." Doctoral thesis, Università degli Studi di Trieste, 2023. https://hdl.handle.net/11368/3042164.
Full textThe aim of electromagnetic (EM) sounding methods in geophysics is to obtain information about the subsurface of the earth by recorded measurements taken at the surface. In particular, the goal is to determine variations in the electrical conductivity of the earth with depth by employing an inversion procedure. In this work we focus on one technique, that consists of placing a magnetic dipole above the surface, composed of a transmitter coil and different couples of adjacent receiver coils. The receiver couples are placed at different distances (offsets) from the transmitter coil. In this setting, the electromagnetic induction effect, encoded in the first-order linear Maxwell’s differential equations, produce eddy alterning currents in the soil which induce response electromagnetic fields, that can be used to determine the conductivity profile of the ground by meaning of an inversion algorithm. A typical inversion strategy consists in an iterative procedure involving the computation of the EM response of a layered model (forward modelling) and the solution of the inverse problem. Then, the algorithm attempts to minimize the mismatch between the measured data and the predicted data, by updating the model parameters at each iteration. By assuming that the local subsurface structures are composed by horizontal and homogeneous layers, general integral solutions of Maxwell equations (i.e., the EM fields) for vertical and horizontal magnetic dipoles, can be derived and represented as Hankel transforms, which contain the subsurface model parameters, i.e., the conductivity and the thickness of each layer. By a mathematical point of view, in general, these Hankel transforms are not analytically computable and therefore it is necessary to employ a numerical scheme. Anyway, the slowly decay of the oscillations determined by the Bessel function makes the problem very difficult to handle, because traditional quadrature rules typically fail to converge. In this work we consider two different approaches. The first one is based on the decomposition of the integrand function in a first function for which the corresponding Hankel transform is known exactly, and an oscillating function decays exponentially. For realistic sets of parameters, the oscillations are quite rapidly damped, and the corresponding integral can be accurately computed by a classical quadrature rule on finite intervals. The second approach consists in the application of a Gaussian quadrature formula. We develop a Gaussian rule for weight functions involving fractional powers, exponentials and Bessel functions of the first kind. Moreover, we derive an analytical approximation of these integrals that has a general validity and allows to overcome the limits of common methods based on the modelling of apparent conductivity in the low induction number (LIN) approximation. Having at disposal a reliable method for evaluating the Hankel transforms, by assuming as forward model a homogeneous layered earth, here we also consider the inverse problem of computing the model parameters (i.e., conductivity and thickness of the layers) from a set of measured field values at different offsets. We focus on the specific case of the DUALEM system. We employ two optimization algorithms. The first one is based on the BFGS line-search method and, in order to reduce as much as possible the number of integral evaluations, the analytic approximation of these integrals is used to have a first estimate of the solution. For the second approach we employ the damped Gauss-Newton method. To avoid the dependence on the initial guess of the iterative procedure, we consider a set of different initial models, and we use each one to solve the optimization problem. The numerical experiments, carried out for the study of river-levees integrity, are obtained by employing a virtual machine equipped with the NVIDIA A100 Tensor Core GPU.
Colomer, Rey Guillem. "Numerical methods for radiative heat transfer." Doctoral thesis, Universitat Politècnica de Catalunya, 2006. http://hdl.handle.net/10803/6691.
Full textEn el capítol 1 s'exposa una breu introducció a la transferència d'energia per radiació, i una explicació de les equacions que la governen. Es tracta de l'equació del transport radiatiu, formulada en termes dels coeficients d'absorció i de dispersió, i l'equació de l'energia. També s'indica quan cal tenir en compte aquest fenòmen, i a més a més, es defineixen totes les magnituds i conceptes que s'han utilitzat en aquesta tesi. També es dóna una breu descripció d'algunes simplificacions que es poden fer a les equacions governants.
El mètode de les radiositats s'explica en el capítol 2. També s'hi descriu un procediment numèric que permet calcular els factors de vista en geometries amb simetria cilíndrica, i es presenten resultats obtinguts amb el mètode descrit. Tot i que aquest capítol està una mica deslligat de la resta de la tesi, l'algoritme ideat per tractar geometries tridimensionals amb un temps computacional molt proper al de geometries bidimensionals, sense un increment de memòria apreciable, dóna uns resultats prou bons com per formar part de la tesi.
El mètode de les ordenades discretes (DOM) es detalla en el capítol 3. L'aspecte més important d'aquest mètode es l'elecció del conjunt d'ordenades per integrar l'equació del transport radiatiu. S'enumeren quines propietats han d'acomplir aquests conjunts. S'hi explica amb detall la discretització de la equació del transport radiatiu, tant en coordenades cartesianes com en cilíndriques. Es presenten també alguns resultats ilustratius obtinguts amb aquest mètode.
En el moment en que es vol resoldre un problema real, cal tenir present que el coeficients d'absorció pot dependre bruscament de la longitud d'ona de la radiació. En aquesta tesi s'ha considerat aquesta dependència amb especial interés, en el capítol 4. Aquest interès ha motivat una recerca bibliogràfica sobre la modelització aquesta forta dependència espectral del coeficient d'absorció. Aquesta recerca s'ha dirigit també a l'estudi dels diferents models numèrics existents capaços d'abordar-la, i de resoldre la equació del transport radiatiu en aquestes condicions. Es descriuen diversos mètodes, i, d'aquests, se n'han implementat dos: el mètode de la suma ponderada de gasos grisos (WSGG), i el mètode de la suma de gasos grisos ponderada per línies espectrals (SLW). S'hi presenten també resultats ilustratius.
S'han realitzat multitud de proves en el codi numèric resultant de l'elaboració d'aquesta tesi. Tenint en compte els resultats obtinguts, es pot dir que els objectius proposats a l'inici de la tesi s'han acomplert. Com a demostració de la utilitat del codi resultant, aquest ha estat integrat en un codi de proposit general (DPC), resultat del treball de molts investigadors en els darrers anys.
Aquesta esmentada integració permet la resolució de problemes combinats de transferència de calor, analitzats en els capítols 5 i 6, on la radiació s'acobla amb la transferència de calor per convecció. La influència de la radiació en la transferència total de calor s'estudia en el capítol 5, publicat a la International Journal of Heat and Mass Transfer, volum 47 (núm. 2), pàg. 257-269, 2004. En el capítol 6, s'analitza l'efecte d'alguns paràmetres del mètode SLW en un problema combinat de transferència de calor. Aquest capítol s'ha enviat a la revista Journal of Quantitative Spectroscopy and Radiative Transfer, per què en consideri la publicació.
The main objective of the present thesis is to study the energy transfer by means of radiation. Therefore, the basic phenomenology of radiative heat transfer has been studied. However, considering the nature of the equation that describes such energy transfer, this work is focussed on the numerical methods which will allow us to take radiation into account, for both transparent and participating media. Being this the first effort within the CTTC ("Centre Tecnològic de Transferència de Calor") research group on this subject, it is limited to simple cartesian and cylindrical geometries.
For this purpose, chapter 1 contains an introduction to radiative energy transfer and the basic equations that govern radiative transfer are discussed. These are the radiative transfer equation, formulated in terms of the absorption and scattering coefficients, and the energy equation. It is also given a discussion on when this mode of energy transfer should be considered. In this chapter are also defined all of the magnitudes and concepts used throughout this work. It ends with a brief description of some approximate methods to take radiation into account.
The Radiosity Irradiosity Method is introduced in chapter 2. In this chapter it is also described a numerical method to calculate the view factors for axial symmetric geometries. The main results obtained in such geometries are also presented. Although a little disconnected from the rest of the present thesis, the algorithm used to handle "de facto"' three dimensional geometries with computation time just a little longer than two dimensional cases, with no additional memory consumption, is considered worthy enough to be included in this work.
In chapter 3, the Discrete Ordinates Method (DOM) is detailed. The fundamental aspect of this method is the choice of an ordinate set to integrate the radiative transfer equation. The characterization of such valuable ordinate sets is laid out properly. The discretization of the radiative transfer equation is explained in etail. The direct solution procedure is also outlined. Finally, illustrative results obtained with the DOM under several conditions are presented.
In the moment we wish to solve real problems, we face the fact that the absorption and scattering coefficients depend strongly on radiation wavelength. In the present thesis, special emphasis has been placed on studying the radiative properties of real gases in chapter 4. This interest resulted on a bibliographical research on how the wavenumber dependence of the absorption coefficient is modeled and estimated. Furthermore, this bibliographical research was focussed also on numerical models able to handle such wavenumber dependence. Several methods are discussed, and two of them, namely the Weighted Sum of Gray Gases (WSGG) and the Spectral Line Weighted sum of gray gases (SLW), have been implemented to perform non gray calculations. Some significant results are shown.
Plenty of tests have been performed to the numerical code that resulted from the elaboration of this thesis. According to the results obtained, the objectives proposed in this thesis have been satisfied. As a demonstration of the usefulness of the implemented code, it has been succesfully integrated to a general purpose computational fluid dynamics code (DPC), fruit of the effort of many researchers during many years.
Results of the above integration lead to the resolution of combined heat transfer problems, that are analyzed in chapters 5 and 6, where radiative heat transfer is coupled to convection heat transfer. The effect of radiation on the total heat transfer is studied in chapter 5, which has been published as International Journal of Heat and Mass Transfer, volume 47 (issue 2), pages 257--269, year 2004. In chapter 6, the impact of some parameters of the SLW model on a combined heat transfer problem is analyzed. This chapter has been submitted for publication at the Journal of Quantitative Spectroscopy and Radiative Transfer.
Marthinsen, Håkon. "Numerical Methods for Optical Interference Filters." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2009. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9966.
Full textWe present the physics behind general optical interference filters and the design of dielectric anti-reflective filters. These can be anti-reflective at a single wavelength or in an interval. We solve the first case exactly for single and multiple layers and then present how the second case can be solved through the minimisation of an objective function. Next, we present several optimisation methods that are later used to solve the design problem. Finally, we test the different optimisation methods on a test problem and then compare the results with those obtained by the OpenFilters computer programme.
Fu, Qi. "Numerical methods for pricing callable bonds." Thesis, University of Macau, 2011. http://umaclib3.umac.mo/record=b2493162.
Full textMayorca, Maria Angelica. "Numerical Methods for Turbomachinery Aeromechanical Predictions." Doctoral thesis, KTH, Kraft- och värmeteknologi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-48418.
Full textQC 20111125
Turbopower, AROMA
Zahedi, Sara. "Numerical Methods for Fluid Interface Problems." Doctoral thesis, KTH, Numerisk analys, NA, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-33111.
Full textQC 20110503
Kuster, Christopher M. "Fast Numerical Methods for Evolving Interfaces." NCSU, 2006. http://www.lib.ncsu.edu/theses/available/etd-04262006-083221/.
Full textAmoignon, Olivier. "Numerical Methods for Aerodynamic Shape Optimization." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-6252.
Full textMorgan, Joanne V. "Numerical methods for macroscopic traffic models." Thesis, University of Reading, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250700.
Full textMason, C. J. "Numerical methods for free boundary problems." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37775.
Full textTamturk, Muhsin. "Ruin probability via several numerical methods." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/42476.
Full textSkorobogatiy, Maksim 1974. "Numerical methods in condensed matter physics." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/82756.
Full textIncludes bibliographical references (leaves 62-63).
by Maksim A. Skorobogatiy.
M.Eng.
Squires, Timothy Richard. "Efficient numerical methods for ultrasound elastography." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:332c7b2b-10c3-4dff-b875-ac1ee2c5d4fb.
Full textOst, Wolfgang. "Numerical Methods for Molecular Quantum Dynamics." Thesis, Uppsala universitet, Institutionen för kemi - Ångström, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-242988.
Full textKressner, Daniel. "Numerical Methods for Structured Matrix Factorizations." [S.l. : s.n.], 2001. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10047770.
Full textKormann, Katharina. "Numerical methods for quantum molecular dynamics." Licentiate thesis, Uppsala : Department of Information Technology, Uppsala University, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-108366.
Full textFrankcombe, Terry James. "Numerical methods in reaction rate theory /." [St. Lucia, Qld.], 2002. http://adt.library.uq.edu.au/public/adt-QU20021128.175205/index.html.
Full textIancu, Aniela Karina. "Numerical methods for pricing basket options." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1078324809.
Full textTitle from first page of PDF file. Document formatted into pages; contains ix, 72 p. : ill. Advisor: Bostwick Wyman, Department of Mathematics. Includes bibliographical references (p. 72).
Goodyer, Christopher Edward. "Adaptive numerical methods for elastohydrodynamic lubrication." Thesis, University of Leeds, 2001. http://etheses.whiterose.ac.uk/1294/.
Full textQuirynen, Rien [Verfasser], and Moritz [Akademischer Betreuer] Diehl. "Numerical simulation methods for embedded optimization." Freiburg : Universität, 2017. http://d-nb.info/112590626X/34.
Full textYan, Shu. "Efficient numerical methods for capacitance extraction based on boundary element method." Texas A&M University, 2005. http://hdl.handle.net/1969.1/3230.
Full textDI, RIENZO ANTONIO FABIO. "Mesoscopic Numerical Methods for Reactive Flows: Lattice Boltzmann Method and Beyond." Doctoral thesis, Politecnico di Torino, 2012. http://hdl.handle.net/11583/2497051.
Full textDe, Martino Giuseppe. "Multi-Value Numerical Modeling for Special Di erential Problems." Doctoral thesis, Universita degli studi di Salerno, 2015. http://hdl.handle.net/10556/1982.
Full textThe subject of this thesis is the analysis and development of new numerical methods for Ordinary Di erential Equations (ODEs). This studies are motivated by the fundamental role that ODEs play in applied mathematics and applied sciences in general. In particular, as is well known, ODEs are successfully used to describe phenomena evolving in time, but it is often very di cult or even impossible to nd a solution in closed form, since a general formula for the exact solution has never been found, apart from special cases. The most important cases in the applications are systems of ODEs, whose exact solution is even harder to nd; then the role played by numerical integrators for ODEs is fundamental to many applied scientists. It is probably impossible to count all the scienti c papers that made use of numerical integrators during the last century and this is enough to recognize the importance of them in the progress of modern science. Moreover, in modern research, models keep getting more complicated, in order to catch more and more peculiarities of the physical systems they describe, thus it is crucial to keep improving numerical integrator's e ciency and accuracy. The rst, simpler and most famous numerical integrator was introduced by Euler in 1768 and it is nowadays still used very often in many situations, especially in educational settings because of its immediacy, but also in the practical integration of simple and well-behaved systems of ODEs. Since that time, many mathematicians and applied scientists devoted their time to the research of new and more e cient methods (in terms of accuracy and computational cost). The development of numerical integrators followed both the scienti c interests and the technological progress of the ages during whom they were developed. In XIX century, when most of the calculations were executed by hand or at most with mechanical calculators, Adams and Bashfort introduced the rst linear multistep methods (1855) and the rst Runge- Kutta methods appeared (1895-1905) due to the early works of Carl Runge and Martin Kutta. Both multistep and Runge-Kutta methods generated an incredible amount of research and of great results, providing a great understanding of them and making them very reliable in the numerical integration of a large number of practical problems. It was only with the advent of the rst electronic computers that the computational cost started to be a less crucial problem and the research e orts started to move towards the development of problem-oriented methods. It is probably possible to say that the rst class of problems that needed an ad-hoc numerical treatment was that of sti problems. These problems require highly stable numerical integrators (see Section ??) or, in the worst cases, a reformulation of the problem itself. Crucial contributions to the theory of numerical integrators for ODEs were given in the XX century by J.C. Butcher, who developed a theory of order for Runge-Kutta methods based on rooted trees and introduced the family of General Linear Methods together with K. Burrage, that uni ed all the known families of methods for rst order ODEs under a single formulation. General Linear Methods are multistagemultivalue methods that combine the characteristics of Runge-Kutta and Linear Multistep integrators... [edited by Author]
XIII n.s.
Harb, Ammar. "Discrete Stability of DPG Methods." PDXScholar, 2016. http://pdxscholar.library.pdx.edu/open_access_etds/2916.
Full textHamed, Maien Mohamed Osman. "On meshless methods : a novel interpolatory method and a GPU-accelerated implementation." Thesis, Nelson Mandela Metropolitan University, 2013. http://hdl.handle.net/10948/d1018227.
Full textBayliss, Martin. "The numerical modelling of elastomers." Thesis, Cranfield University, 2003. http://hdl.handle.net/1826/87.
Full textPiqueras, García Miguel Ángel. "Numerical Methods for Multidisciplinary Free Boundary Problems: Numerical Analysis and Computing." Doctoral thesis, Universitat Politècnica de València, 2018. http://hdl.handle.net/10251/107948.
Full textMany problems in science and engineering are formulated as partial differential equations (PDEs). If the boundary of the domain where these equations are to be solved is not known a priori, we face "Free-boundary problems", which are characteristic of non-time dependent stationary systems; besides, we have "Moving-boundary problems" in temporal evolution processes, where the border changes over time. The solution to these problems is given by the expression of the dependent variable(s) of PDE(s), together with the function that determines the position of the boundary. Since the analytical solution of this type of problems is lacked in most cases, it is necessary to resort to numerical methods that allow an accurate enough solution to be obtained, and which also maintain the qualitative properties of the solution(s) of the continuous model. This work approaches the numerical study of some moving-boundary problems that arise in different disciplines. The applied methodology consists of two successive steps: firstly, the so-called Landau transformation, or "Front-fixing transformation", which is used in the PDE(s) model to maintain the boundary of the domain immobile; later, we proceed to its discretization with a finite difference scheme. Different numerical schemes are obtained and implemented through the MATLAB computational tool. Properties of the scheme and the numerical solution (positivity, stability, consistency, monotonicity, etc.) are studied by an exhaustive numerical analysis. The first chapter of this work reports the state of the art of the field under study, justifies the need to adapt numerical methods to this type of problem, and briefly describes the methodology used in our approach. Chapter 2 presents a problem in Mathematical Biology that consists in determining over time the evolution of an invasive species population that spreads in a habitat. This problem is modelled by a diffusion-reaction equation linked to a Stefan-type condition. The results of the numerical analysis confirm the existence of a spreading-vanishing dichotomy in the long-term evolution of the population density of the invasive species. In particular, it is possible to determine the value of the coefficient of the Stefan condition that separates the propagation behaviour from extinction. Chapters 3 and 4 focus on a problem of Concrete Chemistry with an interest in Civil Engineering: the carbonation of concrete, an evolutionary phenomenon that leads to the progressive degradation of the affected structure and its eventual ruin if preventive measures are not taken. Chapter 3 considers a system of two parabolic type PDEs with two unknowns. For its resolution, the initial and boundary conditions have to be considered together with the Stefan conditions on the carbonation front. The numerical analysis results agree with those obtained in a previous theoretical study. The dynamics of the concentrations and the moving boundary confirm the long-term behaviour of the evolution law for the moving boundary as a "square root of time". Chapter 4 considers a more general model than the previous one, which includes six chemical species, defined in both the carbonated and non-carbonated zones, whose concentrations have to be found. Chapter 5 addresses a heat transfer problem that appears in various industrial processes; in this case, the solidification of metals in casting processes, where the solid phase advances and liquid reduces until it is depleted. The moving boundary (the solidification front) separates both phases. Its position in each instant is the variable to be determined together with the temperature profiles in both phases. After suitable transformation, discretization is carried out to obtain a finite difference scheme to be implemented. The process was subdivided into three temporal stages to deal with the singularities associated with the moving boundary position in the initialisation and depletion stages.
Multitud de problemes en ciència i enginyeria es plantegen com a equacions en derivades parcials (EDPs). Si la frontera del recinte on eixes equacions han de satisfer-se es desconeix a priori, es parla de "Problemas de frontera lliure", propis de sistemes estacionaris no dependents del temps, o bé de "Problemas de frontera mòbil", associats a problemes d'evolució temporal, on la frontera canvia amb el temps. Atés que este tipus de problemes manca en la majoria dels casos de solució analítica coneguda, es fa precís recórrer a mètodes numèrics que permeten obtindre una solució prou aproximada a l'exacta, i que a més mantinga propietats qualitatives de la solució del model continu d'EDP(s). En aquest treball s'ha abordat l'estudi numèric d'alguns problemes de frontera mòbil provinents de diverses disciplines. La metodologia aplicada consta de dos passos successius: en primer lloc, s'aplica l'anomenada transformació de Landau o "Front-fixing transformation" al model en EDP(s) a fi de mantindre immòbil la frontera del domini; posteriorment, es procedix a la seva discretització a través d'un esquema en diferències finites. D'ací s'obtenen esquemes numèrics que s'implementen per mitjà de la ferramenta informàtica MATLAB. Per mitjà d'una exhaustiva anàlisi numèrica, s'estudien propietats de l'esquema i de la solució numèrica (positivitat, estabilitat, consistència, monotonia, etc.). En el primer capítol d'aquest treball es revisa l'estat de l'art del camp objecte d'estudi, es justifica la necessitat de disposar de mètodes numèrics adaptats a aquest tipus de problemes i es descriu breument la metodologia emprada en el nostre enfocament. El Capítol 2 es dedica a un problema pertanyent a la Biologia Matemàtica i que consistix a determinar l'evolució en el temps de la distribució de la població d'una espècie invasora que es propaga en un hàbitat. Este model consistix en una equació de difusió-reacció unida a una condició tipus Stefan, que relaciona les funcions solució i frontera mòbil a determinar. Els resultats de l'anàlisi numèrica confirmen l'existència d'una dicotomia propagació-extinció en l'evolució a llarg termini de la densitat de població de l'espècie invasora. En particular, s'ha pogut precisar el valor del coeficient de la condició de Stefan que separa el comportament de propagació del d'extinció. Els Capítols 3 i 4 se centren en un problema de Química del Formigó amb interés en Enginyeria Civil: el procés de carbonatació del formigó, fenomen evolutiu que comporta la degradació progressiva de l'estructura afectada i finalment la seua ruïna, si no es prenen mesures preventives. En el Capítol 3 es considera un sistema de dos EDPs de tipus parabòlic amb dos incògnites. Per a la seua resolució, cal considerar a més, les condicions inicials, les de contorn i les de tipus Stefan en la frontera. Els resultats de l'anàlisi numèrica s'ajusten als obtinguts en un estudi teòric previ. S'han dut a terme experiments numèrics, comprovant la tendència de la llei d'evolució de la frontera mòbil cap a una funció del tipus "arrel quadrada del temps". En el Capítol 4 es considera un model més general, en el que intervenen sis espècies químiques les concentracions de les quals cal trobar, i que es troben tant en la zona carbonatada com en la no carbonatada. En el Capítol 5 s'aborda un problema de transmissió de calor que apareix en diversos processos industrials; en aquest cas, en el refredament durant la bugada de metall fos, on la fase sòlida avança i la líquida es va extingint. La frontera mòbil (front de solidificació) separa ambdues fases, sent la seua posició en cada instant la variable a determinar, junt amb les temperatures en cada una de les dos fases. Després de l'adequada transformació i discretització, s'implementa un esquema en diferències finites, subdividint el procés en tres estadis temporals, per tal de tractar les singularitats asso
Piqueras García, MÁ. (2018). Numerical Methods for Multidisciplinary Free Boundary Problems: Numerical Analysis and Computing [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/107948
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Postell, Floyd Vince. "High order finite difference methods." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/28876.
Full textBoyanova, Petia. "On Numerical Solution Methods for Block-Structured Discrete Systems." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-173530.
Full textZangor, Roxana Ioana Lutoborski A. "Numerical methods for smooth, detectable image perturbations." Related Electronic Resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2003. http://wwwlib.umi.com/cr/syr/main.
Full textHandari, Bevina D. "Numerical methods for SDEs and their dynamics /." [St. Lucia, Qld.], 2002. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17145.pdf.
Full textJohansson, Christer. "Numerical Methods for Ports in Closed Waveguides." Licentiate thesis, KTH, Numerical Analysis and Computer Science, NADA, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1652.
Full textWaveguides are used to transmit electromagnetic signals.Their geometry is typically long and slender their particularshape can be used in the design of computational methods. Onlyspecial modes are transmitted and eigenvalue and eigenvectoranalysis becomes important.
We develop a .nite-element code for solving theelectromagnetic .eld problem in closed waveguides .lled withvarious materials. By discretizing the cross-section of thewaveguide into a number of triangles, an eigenvalue problem isderived. A general program based on Arnoldis method andARPACK has been written using node and edge elements toapproximate the .eld. A serious problem in the FEM was theoccurrence of spurious solution, that was due to impropermodeling of the null space of the curl operator. Therefore edgeelements has been chosen to remove non physical spurioussolutions that arises.
Numerical examples are given for homogeneous andinhomogeneous waveguides, in the homogeneous case the resultsare compared to analytical solutions and the right order ofconvergence is achieved. For the more complicated inhomogeneouswaveguides with and without striplines, comparison has beendone with results found in literature together with gridconvergence studies.
The code has been implemented to be used in an industrialenvironment, together with full 3-D time and frequency domainsolvers. The2-D simulations has been used as input for full3-D time domain simulations, and the results have been comparedto what an analytical input would give.
Linell, Mattias. "Pricing American Put Options using Numerical Methods." Thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120038.
Full textHaber, René. "Numerical methods for density of states calculations." Master's thesis, Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200801991.
Full textZhao, Jing Ya. "Numerical methods for pricing Bermudan barrier options." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592939.
Full textEngblom, Stefan. "Numerical Solution Methods in Stochastic Chemical Kinetics." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-9342.
Full textd'Halluin, Yann. "Numerical Methods for Real Options in Telecommunications." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1206.
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