Dissertations / Theses: 'Finite differences'

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Floyd, Stewart Allen. "A qualitative analysis of finite difference equations in R[superscript n]." Thesis, Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/29441.

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蔡景華 and King-wah Choi. "Finite difference modelling of estuarine hydrodynamics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1985. http://hub.hku.hk/bib/B30425153.

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Hayman, Kenneth John. "Finite-difference methods for the diffusion equation." Title page, table of contents and summary only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phh422.pdf.

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Ampadu, Ebenezer. "Implementation of some finite difference methods for the pricing of derivatives using C++ programming." Link to electronic thesis, 2007. http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/.

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Demirayak, Murat Neslitürk Ali İhsan. "Analysis Of Finite Difference Methods For Convection-Diffusion Problem/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/matematik/T000481.pdf.

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Ağıroğlu, İzzet Onur Tanoğlu Gamze. "An application of the finite differences method to a dynamical interface problem/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/matematik/T000445.pdf.

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Trojan, Alice von. "Finite difference methods for advection and diffusion." Title page, abstract and contents only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phv948.pdf.

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Includes bibliographical references (leaves 158-163). Concerns the development of high-order finite-difference methods on a uniform rectangular grid for advection and diffuse problems with smooth variable coefficients. This technique has been successfully applied to variable-coefficient advection and diffusion problems. Demonstrates that the new schemes may readily be incorporated into multi-dimensional problems by using locally one-dimensional techniques, or that they may be used in process splitting algorithms to solve complicatef time-dependent partial differential equations.

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Choi, King-wah. "Finite difference modelling of estuarine hydrodynamics /." [Hong Kong] : University of Hong Kong, 1985. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1232503X.

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9

Reimers, Mark Allan. "Hyper-finite methods for multi-dimensional stochastic processes." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/27515.

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In this thesis we introduce Non-Standard Methods, in particular the use of hyperfinite difference equations, to the study of space-time random processes. We obtain a new existence theorem in the spirit of Keisler (1984) for the one dimensional heat equation forced non-linearly by white noise. We obtain several new results on the sample path properties of the Critical Branching Measure Diffusion, and show that in one dimension it has a density which satisfies a non-linearly forced heat equation. We also obtain results on the dimension of the support of the Fleming-Viot Process.
Science, Faculty of
Mathematics, Department of
Graduate

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Kama, Phumezile. "Non-standard finite difference methods in dynamical systems." Thesis, Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-07132009-163422.

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Dea, John R. "High-order non-reflecting boundary conditions for the linearized Euler equations." Monterey, Calif. : Naval Postgraduate School, 2008. http://edocs.nps.edu/npspubs/scholarly/theses/2008/Sept/08Sep%5FDea%5FPhD.pdf.

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Dissertation (Ph.D. in Applied Mathematics)--Naval Postgraduate School, September 2008.
Dissertation Advisor(s): Neta, Beny. "September 2008." Description based on title screen as viewed on November 6, 2008. Includes bibliographical references (p. 161-170). Also available in print.

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Johnson, Fen Rui. "A study of finite and linear elasticity." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1096.

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Chirvasa, Mihaela. "Finite difference methods for 1st Order in time, 2nd order in space, hyperbolic systems used in numerical relativity." Phd thesis, Universität Potsdam, 2010. http://opus.kobv.de/ubp/volltexte/2010/4213/.

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This thesis is concerned with the development of numerical methods using finite difference techniques for the discretization of initial value problems (IVPs) and initial boundary value problems (IBVPs) of certain hyperbolic systems which are first order in time and second order in space. This type of system appears in some formulations of Einstein equations, such as ADM, BSSN, NOR, and the generalized harmonic formulation. For IVP, the stability method proposed in [14] is extended from second and fourth order centered schemes, to 2n-order accuracy, including also the case when some first order derivatives are approximated with off-centered finite difference operators (FDO) and dissipation is added to the right-hand sides of the equations. For the model problem of the wave equation, special attention is paid to the analysis of Courant limits and numerical speeds. Although off-centered FDOs have larger truncation errors than centered FDOs, it is shown that in certain situations, off-centering by just one point can be beneficial for the overall accuracy of the numerical scheme. The wave equation is also analyzed in respect to its initial boundary value problem. All three types of boundaries - outflow, inflow and completely inflow that can appear in this case, are investigated. Using the ghost-point method, 2n-accurate (n = 1, 4) numerical prescriptions are prescribed for each type of boundary. The inflow boundary is also approached using the SAT-SBP method. In the end of the thesis, a 1-D variant of BSSN formulation is derived and some of its IBVPs are considered. The boundary procedures, based on the ghost-point method, are intended to preserve the interior 2n-accuracy. Numerical tests show that this is the case if sufficient dissipation is added to the rhs of the equations.
Diese Doktorarbeit beschäftigt sich mit der Entwicklung numerischer Verfahren für die Diskretisierung des Anfangswertproblems und des Anfangs-Randwertproblems unter Einsatz von finite-Differenzen-Techniken für bestimmte hyperbolischer Systeme erster Ordnung in der Zeit und zweiter Ordnung im Raum. Diese Art von Systemen erscheinen in einigen Formulierungen der Einstein'schen-Feldgleichungen, wie zB. den ADM, BSSN oder NOR Formulierungen, oder der sogenanten verallgemeinerten harmonischen Darstellung. Im Hinblick auf das Anfangswertproblem untersuche ich zunächst tiefgehend die mathematischen Eigenschaften von finite-Differenzen-Operatoren (FDO) erster und zweiter Ordnung mit 2n-facher Genaugigkeit. Anschließend erweitere ich eine in der Literatur beschriebene Methode zur Stabilitätsanalyse für Systeme mit zentrierten FDOs in zweiter und vierter Genauigkeitsordung auf Systeme mit gemischten zentrierten und nicht zentrierten Ableitungsoperatoren 2n-facher Genauigkeit, eingeschlossen zusätzlicher Dämpfungsterme, wie sie bei numerischen Simulationen der allgemeinen Relativitätstheorie üblich sind. Bei der Untersuchung der einfachen Wellengleichung als Fallbeispiel wird besonderes Augenmerk auf die Analyse der Courant-Grenzen und numerischen Geschwindigkeiten gelegt. Obwohl unzentrierte, diskrete Ableitungsoperatoren größere Diskretisierungs-Fehler besitzen als zentrierte Ableitungsoperatoren, wird gezeigt, daß man in bestimmten Situationen eine Dezentrierung des numerischen Moleküls von nur einem Punkt bezüglich des zentrierten FDO eine höhere Genauigkeit des numerischen Systems erzielen kann. Die Wellen-Gleichung in einer Dimension wurde ebenfalls im Hinblick auf das Anfangswertproblem untersucht. In Abhängigkeit des Wertes des sogenannten Shift-Vektors, müssen entweder zwei (vollständig eingehende Welle), eine (eingehende Welle) oder keine Randbedingung (ausgehende Welle) definiert werden. In dieser Arbeit wurden alle drei Fälle mit Hilfe der 'Ghost-point-methode' numerisch simuliert und untersucht, und zwar auf eine Weise, daß alle diese Algorithmen stabil sind und eine 2n-Genauigkeit besitzen. In der 'ghost-point-methode' werden die Evolutionsgleichungen bis zum letzen Punkt im Gitter diskretisiert unter Verwendung von zentrierten FDOs und die zusätzlichen Punkte die am Rand benötigt werden ('Ghost-points') werden unter Benutzung von Randwertbedingungen und Extrapolationen abgeschätzt. Für den Zufluß-Randwert wurde zusätzlich noch eine andere Implementierung entwickelt, welche auf der sogenannten SBP-SAT (Summation by parts-simulatanous approximation term) basiert. In dieser Methode werden die diskreten Ableitungen durch Operatoren angenähert, welche die 'Summation-by-parts' Regeln erfüllen. Die Randwertbedingungen selber werden in zusätzlichen Termen integriert, welche zu den Evolutionsgleichnungen der Punkte nahe des Randes hinzuaddiert werden und zwar auf eine Weise, daß die 'summation-by-parts' Eigenschaften erhalten bleiben. Am Ende dieser Arbeit wurde noch eine eindimensionale (kugelsymmetrische) Version der BSSN Formulierung abgeleitet und einige physikalisch relevanten Anfangs-Randwertprobleme werden diskutiert. Die Randwert-Algorithmen, welche für diesen Fall ausgearbeitet wurden, basieren auf der 'Ghost-point-Methode' and erfüllen die innere 2n-Genauigkeit solange genügend Reibung in den Gleichungen zugefügt wird.

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14

Steinle, Peter John. "Finite difference methods for the advection equation /." Title page, table of contents and abstract only, 1993. http://web4.library.adelaide.edu.au/theses/09PH/09phs8224.pdf.

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15

Persson, Jonas. "Accurate Finite Difference Methods for Option Pricing." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7097.

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16

Ghosh, Swarnava Ghosh. "Orbital-free density functional theory using higher-order finite differences." Thesis, Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53603.

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Density functional theory (DFT) is not only an accurate but also a widely used theory for describing the quantum-mechanical electronic structure of matter. In this approach, the intractable problem of interacting electrons is simplified to a tractable problem of non-interacting electrons moving in an effective potential. Even with this simplification, DFT remains extremely computationally expensive. In particular, DFT scales cubically with respect to the number of atoms, which restricts the size of systems that can be studied. Orbital free density functional theory (OF-DFT) represents a simplification of DFT applicable to metallic systems that behave like a free-electron gas. Current implementations of OF-DFT employ the plane-wave basis, the global nature of the basis prevents the efficient use of modern high-performance computer archi- tectures. We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a gener- alized framework suitable for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we develop a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In doing so, we make the calculation of the electronic ground-state and forces on the nuclei amenable to computations that altogether scale linearly with the number of atoms. We develop a parallel implementation of our method using Portable, Extensible Toolkit for scientific computations (PETSc) suite of data structures and routines. The communication between processors is handled via the Message Passing Interface(MPI). We implement this formulation using the finite-difference discretization, us- ing which we demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson mixing. We verify the accuracy of our results by comparing the energies and forces with plane-wave methods for selected examples, one of which is the vacancy formation energy in Aluminum. Overall, we demonstrate that the proposed formulation and implementation is an attractive choice for performing OF-DFT calculations.

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17

Wang, Xi. "Finite Differences Based on Radial Basis Functions to Price Options." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-243518.

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Sena, Giuseppe A. (Giuseppe Antonio). "Very large scale finite differences in modeling of seismic waves." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/58055.

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19

Ashworth, Eileen. "Heat flow into underground openings: Significant factors." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185768.

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This project investigates the heat flow from the rock into ventilating airways by studying various parameters. Two approaches have been used: laboratory measurement of thermal properties to study their variation, and analytic and numerical models to study the effect of these variations on the heat flow. Access to a heat-flux system and special treatment of contact resistance has provided the opportunity to study thermal conductivity as a function of moisture contained in rock specimens. For porous sandstone, tuff, and concretes, thermal conductivity can double when the specimens are soaked; the functional dependence of conductivity on moisture for the first two cases is definitely non-linear. Five previous models for conductivity as a function of porosity are shown not to explain this new phenomenon. A preliminary finite element model is proposed which explains the key features. Other variations of conductivity with applied pressure, location, constituents, weathering or other damage, and anisotropy have been measured. In the second phase of the research, analytical and numerical methods have been employed to consider the effects of the variation in the thermal properties plus the use of insulation on the heat flow from the rock into the ventilated and cooled airways. Temperature measurements taken in drill holes at a local mine provide confirmation for some of the models. Results have been provided in a sensitivity analysis mode so that engineers working on other projects can see which parameters would require more detailed consideration. The thermal conductivity of the rock close to the airways is a key factor in affecting heat loads. Dewatering and the use of insulation, such as lightweight foamed shotcretes, are recommended.

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Werpers, Jonatan. "Numerical simulation of solitons in the nerve axon using finite differences." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-234383.

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A High-order accurate finite difference scheme is derived for a non-linear soliton model of nerve signal propagation in axons. Boundary conditions yielding well-posed problems are suggested and included in the scheme using a penalty technique. Stability is shown using the summation-by-parts framework for a frozen parameter version of the non-linear problem.

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Lønsethagen, Simen Andreas Andreassen. "Krylov Subspace Accelerated Algebraic Multigrid for Mimetic Finite Differences on GPUs." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19328.

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The topic of this thesis is GPU accelerated sparse linear algebra for subsurface reservoir modeling. Numerical techniques for reservoir sim- ulations are described and we present the open source reservoir simula- tion software toolbox MRST. We discuss some of the challenges related to linear algebra and reservoir simulation. Furthermore, we discuss the possibility GPU-acceleraing the linear algebra for reservoir simulation, and implement a GPU based CG solver preconditioned with AMG for MRST, using the open source linear algebra library CUSP.

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Sjöberg, Alexander. "Adaptive finite differences to price European options under the Bates model." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-206899.

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This thesis presents the pricing of European options under the Bates model, using adaptivity in order to efficiently distribute the grid points in space. For a fixed number of grid points the size of the absolute error, when using the adaptive approach, is reduced compared to the corresponding equidistant grid. Since the adaptive method needs less grid points for a certain error, the linear system of equations that needs to be solved becomes smaller and the memory costs are reduced. The implementation does not rest upon heavy optimization or parallelization theory, but nevertheless it solves the problem flawlessly and the adaptive method outperforms the equidistant method regarding computational time when keeping the error at a predefined level.

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Dumanois, Stephane. "Least Squares Radial Basis Function generated Finite Differences for Option Pricing." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-312815.

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Svärd, Magnus. "Stable high-order finite difference methods for aerodynamics /." Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4621.

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Sousa, Ercília. "Finite differences for the convection-diffusion equation : on stability and boundary conditions." Thesis, University of Oxford, 2001. http://ora.ox.ac.uk/objects/uuid:8369da31-2229-4e05-846c-de3072ac1a37.

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The solution of convection-diffusion problems is a challenging task for numerical methods because of the nature of the governing equation, which includes a non-dissipative component and a dissipative component. Once the convection-diffusion equation is discretised, it is usual to observe oscillations in the computed solution regardless of whether these might be expected in the original physical situation. Mostly these oscillations are the result of numerical instability. This thesis centres on this fundamental difficulty: the numerical stability of finite difference discretisation of a convection-diffusion equation. The existence of an exact evolution operator for the constant coefficient convection diffusion problem is the framework we use to derive new finite difference schemes in one and two dimensions and also, when a high-order scheme is considered, to derive numerical boundary conditions. The influence of numerical boundary conditions on the stability of a general scheme is one of the main themes. The stability analysis is done mostly by using the von Neumann method and the matrix method. The Godunov-Ryabenkii theory is also applied to the one dimensional case. In two dimensions we deduce different forms of second-order (Lax-Wendroff) schemes and third-order (Quickest) schemes. We apply some of those schemes to a Navier-Stokes problem by running experiments to illustrate the practical stability region, showing how results from a simpler case presented in previous chapters carry over to the more complex case.

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Sharp, Richard Paul. "Computational approaches for diffusive light transport finite-elements, grid adaption, and error estimation /." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1154705561.

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Dong, Hao. "Adaptive moving grid method to two-phase flow problesm." HKBU Institutional Repository, 2011. http://repository.hkbu.edu.hk/etd_ra/1275.

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Meagher, Timothy P. "A New Finite Difference Time Domain Method to Solve Maxwell's Equations." PDXScholar, 2018. https://pdxscholar.library.pdx.edu/open_access_etds/4389.

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We have constructed a new finite-difference time-domain (FDTD) method in this project. Our new algorithm focuses on the most important and more challenging transverse electric (TE) case. In this case, the electric field is discontinuous across the interface between different dielectric media. We use an electric permittivity that stays as a constant in each medium, and magnetic permittivity that is constant in the whole domain. To handle the interface between different media, we introduce new effective permittivities that incorporates electromagnetic fields boundary conditions. That is, across the interface between two different media, the tangential component, Er(x,y), of the electric field and the normal component, Dn(x,y), of the electric displacement are continuous. Meanwhile, the magnetic field, H(x,y), stays as continuous in the whole domain. Our new algorithm is built based upon the integral version of the Maxwell's equations as well as the above continuity conditions. The theoretical analysis shows that the new algorithm can reach second-order convergence O(∆x2)with mesh size ∆x. The subsequent numerical results demonstrate this algorithm is very stable and its convergence order can reach very close to second order, considering accumulation of some unexpected numerical approximation and truncation errors. In fact, our algorithm has clearly demonstrated significant improvement over all related FDTD methods using effective permittivities reported in the literature. Therefore, our new algorithm turns out to be the most effective and stable FDTD method to solve Maxwell's equations involving multiple media.

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29

Stephan, Andrew Jon Eugene. "Convection Driven Dynamos in Rotating Spheres." Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/14763.

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Of the objects in the solar system the Earth, Mercury, Jupiter, Saturn, Uranus, Neptune, Ganymede, and the Sun exhibit a magnetic field. These magnetic fields are believed to be generated by the magnetohydrodynamic dynamo process, in which current, generated as electrically conducting fluid crosses magnetic field lines, regenerates the magnetic field. Although most of the bodies listed above are believed to consist of a fluid outer core with a solid inner core, i.e. a spherical shell geometry, the full sphere dynamo problem is of physical interest as the dynamo of the early Earth, the ancient dynamo of Mars, and possibly Venus, the Moon and (currently) Mercury, are believed to have had no solid inner core. In this thesis we consider numerically the problem of magnetic field generation in a full sphere of rotating uniformly conducting fluid driven by a volumetric heat source. In order to numerically integrate the governing system of equations we combine the poloidal-toroidal field representation of Elsasser (1946) and Bullard&Gellman (1954) with an implicit/explicit multi-step Gear timestepping method and finite differences in radius. For the implicit radial differencing we develop a generalised compact finite-difference method which results in high order/low bandwidth timestepping systems, and we demonstrate that this method is competitive with other finite-difference methods: standard finite differences, Padé finite-differences, and the combined compact finitedifference schemes of Chu&Fan (1998). The numerical integrator is applied to three physical problems of interest. The first is kinematic dynamo action in a sphere. We investigate the possibility of dynamo action for flows with a missing component in spherical polar coordinates and find the growth rates are highly sensitive to changes in the truncation level. Nevertheless, we do find a working kinematic dynamo with axisymmetric velocity with no azimuthal component which demonstrates convincing convergence. The second problem we consider is that of thermal convection in the absence of a magnetic field in a rotating sphere. We fix the Ekman and Prandtl number (E; Pr) = (5 10¿4; 0:7) and obtain an estimate of the critical Rayleigh number Rac for the onset of convection, and describe the main characteristic of the flow for the convection solutions for Ra 1:4 Rac and Ra 5 Rac. These solutions are primarily for comparison for solutions computed in the third problem: dynamical dynamo action in a rotating sphere. The primary aim is to survey dynamo solutions for the fixed Ekman and Prandtl numbers (E; Pr) = (5 10¿4; 0:7), for magnetic Prandtl number varied from 1 to 40 and the modified Rayleigh number varied up to a few times the critical value for the onset of convection. We consider the solutions through the lens of dynamo scaling laws, but find no universally satisfactory theoretical or numerical scaling law. We also consider a weak/strong field classification of the solutions, finding highly localised force balances. We finish by considering three solutions in detail which represent three distinct classes of dynamo solution: an oscillating dipolar solution, an oscillating quadrupolar solution and a chaotic solution which oscillates between two different hemispherical states. Finally, we develop a first approach to the problem of dynamo action in a fluid sphere as it cools (with no internal heat source), and we present some first convective solutions which function exactly as we expect: the convection dieing down as the fluid cools.

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Bencharif, Nasr-Eddine. "Linear and nonlinear deflection analysis of thick rectangular plates using finite differences." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/10984.

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Variational methods are widely used for the solution of complex differential equations in mechanics for which exact solutions are not possible. The finite difference method, although well known as an efficient numerical method was applied in the past only for the solution of linear and nonlinear thin plates. In the present study, the suitability of the method for the solution of nonlinear deflection of thick plates is studied for the first time. While there is major differences between small deflection and large deflection plate theories, the former can be treated as a particular case of the latter, when the centre deflection of the plate is less than or equal to 0.2-0.25 of the thickness of the plate. The finite difference method as applied here is a modified finite difference approach to the ordinary finite difference method generally used for the solution of thin plate problems. In this thesis thin plates are treated as a particular case of the corresponding thick plate when the boundary conditions of the plates are taken into account. The method is first applied to investigate the deflection behaviour of square clamped and simply supported square isotropic thick plates. After the validity of the method is established, it is then extended to the solution of rectangular thick plates of various aspect ratios and thicknesses. Generally, beginning with the use of a limited number of mesh sizes for a given plate aspect ratio and boundary conditions, a general solution of the problem including the investigation of accuracy and convergence was extended to rectangular thick plates by providing more detailed functions satisfying the rectangular mesh sizes generated automatically by the programme. Whenever possible results of the present method are compared with the existing solutions in the technical literature obtained by much more laborious methods and close agreements are found. Significant amounts of results presented herein are not currently available in the technical literature for various plate aspect ratios and Poisson's ratios. The submatrices involved in the formation of the finite difference equations from the governing differential equations forming the general system are generated directly by the computer programme. The subroutine SOLINV from the second directed method as developed and illustrated in Chapter V takes care of the inversion of the general matrix. The subroutine developed by the author has been proven to be more efficient than the former methods known for the computation of linear simultaneous equations [61]. Simplicity in formulation and quick convergence are the obvious advantages of the finite difference formulation developed here for small and large deflection analysis of thick plate in comparison with other numerical methods requiring extensive computer facilities.

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Vasyliv, Yaroslav V. "Development of general finite differences for complex geometries using immersed boundary method." Thesis, Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54425.

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In meshfree methods, partial differential equations are solved on an unstructured cloud of points distributed throughout the computational domain. In collocated meshfree methods, the differential operators are directly approximated at each grid point based on a local cloud of neighboring points. The set of neighboring nodes used to construct the local approximation is determined using a variable search radius. The variable search radius establishes an implicit nodal connectivity and hence a mesh is not required. As a result, meshfree methods have the potential flexibility to handle problem sets where the computational grid may undergo large deformations as well as where the grid may need to undergo adaptive refinement. In this work we develop the sharp interface formulation of the immersed boundary method for collocated meshfree approximations. We use the framework to implement three meshfree methods: General Finite Differences (GFD), Smoothed Particle Hydrodynamics (SPH), and Moving Least Squares (MLS). We evaluate the numerical accuracy and convergence rate of these methods by solving the 2D Poisson equation. We demonstrate that GFD is computationally more efficient than MLS and show that its accuracy is superior to a popular corrected form of SPH and comparable to MLS. We then use GFD to solve several canonic steady state fluid flow problems on meshfree grids generated using uniform and variable radii Poisson disk algorithm.

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Mettot, Clément. "Linear stability, sensitivity, and passive control of turbulent flows using finite differences." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/92/19/08/PDF/Manuscript_Clement_Mettot.pdf.

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La contribution majeure de cette thèse consiste en un formalisme et une méthodologie permettant de réaliser une analyse de stabilité globale des écoulements turbulents. La dynamique de ces écoulements est modélisée à l'aide des équations moyennées RANS, on s'intéresse ainsi à l'évolution des grandes échelles turbulentes. Un formalisme global est adopté permettant d'analyser des écoulements complexes. Une approche de type discrète est proposée, où les équations sont d'abord discrétisées puis linéarisées par différences finies. Cette approche permet d'adopter une stratégie générique vis à vis du système d'équations utilisées, comme le choix d'un modèle turbulent, et évite une linéarisation analytique fastidieuse des équations. Par ailleurs, cette méthode permet également l'utilisation systématique d'un code de simulation numérique afin de réaliser une étude de stabilité linéaire. Enfin, on démontre que l'analyse de la sensibilité à des perturbations stationnaires peut être réalisée grâce à ce formalisme et ce pour des écoulements laminaires et turbulents. Cette analyse détermine les zones où un contrôle stationnaire permettrait de réduire les instationnarités observées, facilitant la conception de stratégies efficaces de contrôle en boucle ouverte. La méthode est testée en premier lieu sur deux écoulements laminaires, où l'on reproduit les résultats obtenus par de précédentes études sur la dynamique d'oscillateur du sillage d'un cylindre bidimensionnel ainsi que sur la dynamique d'amplificateur de bruit d'une couche limite. La robustesse et la validité de notre méthode sont ensuite analysées sur un cas d'écoulement compressible et turbulent dans une cavité profonde. La précision des gradients de sensibilité est vérifiée, et la physique de l'écoulement, modes instables, propriétés acoustiques, impact de la modélisation de la turbulence, est détaillée. Afin de mieux appréhender la portabilité ainsi que la valeur ajoutée de notre méthode, on présentera ensuite trois cas d'études réalisées à l'aide de nos outils. On s'intéressera en premier lieu au phénomène de buffet sur un profil bidimensionnel, puis on présentera des résultats obtenus sur la caractérisation comme amplificateur de bruit d'un cas d'interaction de choc-couche limite, enfin une analyse du screech dans les jets sous détendus sera proposée. Enfin, on présente en dernier lieu une étude de la dynamique turbulente du sillage derrière un cylindre en forme de D
The contribution of this Ph. D consists in a formalism and a methodology to perform linear stability analysis of turbulent flows. The flow dynamics is modelled using the RANS equations closed with a turbulence model, and we focus on the instabilities associated with the large scale structures of turbulence. A global formulation is adopted so as to allow complex geometries analysis. A discrete framework is considered, where the equations are first discretized and then linearized. In particular, the linearization is performed using finite differences. This procedure ensures the generic character of the method regarding the system of equations such as the turbulence model for example, and avoids tedious analytical linearization. Furthermore, it allows to use a numerical code in a black-box manner in order to perform linear stability analysis. Finally, we demonstrate that the sensitivity gradients can be computed within this framework for both laminar and turbulent flows. Sensitivity analysis carries valuable information regarding the location where steady control means can affect the flow unsteadiness, enabling the design of robust strategies for open loop control. The method is first tested on two laminar cases, reproducing former studies concerned with the oscillators dynamics of the wake behind a two dimensional cylinder, and the characterization of a laminar boundary layer as a noise amplifier. The robustness and validity of our procedure is then extensively studied on a compressible turbulent flow over a deep cavity. Numerical validations are performed, ensuring the correctness of our sensitivity gradients up to 3\%, and the flow physics, including unstable mode analysis, acoustics, impact of turbulence modeling, is analysed. In order to enhance the portability and the valuable information carried out by our method, we present several preliminary studies that were performed using our formalism. First, we revisit the transonic buffet over an airfoil, the noise amplifier dynamics of a turbulent shock-boundary layer interaction is then characterized and we conclude with an analysis of the screech phenomenon in under-expanded jets. Finally, we conclude this work by studying the turbulent wake behind a D-shaped cylinder, and show the potential of our method for industrial applications

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33

Kung, Christopher W. "Development of a time domain hybrid finite difference/finite element method for solutions to Maxwell's equations in anisotropic media." Columbus, Ohio : Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1238024768.

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34

Tan, Zhijun. "Moving mesh finite volume method and its applications." HKBU Institutional Repository, 2005. http://repository.hkbu.edu.hk/etd_ra/592.

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35

He, Jianqing. "Finite difference time domain simulation of subpicosecond semiconductor optical devices." Diss., This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-05042006-164534/.

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36

Teramoto, Elias Hideo [UNESP]. "Caracterização hidrogeológica e simulação numérica de fluxo em uma região situada no distrito industrial de Paulínia (SP)." Universidade Estadual Paulista (UNESP), 2007. http://hdl.handle.net/11449/92749.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Em área contaminada por hidrocarbonetos, situada no município de Paulínia, a migração dos contaminantes e a eficiência do sistema de bombeamento são governadas pela heterogeneidade litológica do aqüífero local, constituído por rochas do Subgrupo Itararé, rochas intrusivas básicas da Formação Serra Geral e por sedimentos cenozóicos correlatos à Formação Rio Claro. Desta forma, o entendimento da heterogeneidade que caracteriza este aqüífero e suas propriedades hidráulicas é essencial para a otimização e o aprimoramento do processo de remediação. Visando delinear o entendimento e a caracterização hidrogeológica local, foi elaborado modelo hidrogeológico conceitual, por meio da integração de dados provenientes de técnicas tradicionais de investigação, tais como métodos geofísicos, monitoramento dos níveis piezométricos de poços de monitoramento, descrições geológicas e análises granulométricas, para entendimento da dinâmica de fluxo local, distribuição litológica do substrato aqüífero e seus valores de condutividade hidráulica. Foram ainda realizadas simulações numéricas de fluxo em regime permanente, utilizando o software Visual Modflow, que emprega o método de diferenças finitas para testar o modelo conceitual concebido. A simulação numérica apresentou excelentes correlações entre os valores de cargas hidráulicas medidas e simuladas e os resultados obtidos permitiram verificar a consistência do modelo conceitual.
In an hydrocarbon contaminated area locate in Paulínia city, lithological heterogeneity of local aquifer controls the migration of contaminant and the efficiency of pump system. The aquifer is composed by sedimentary rocks of Itararé Sub-group, basic intrusive of Serra Geral Formation and cenozoic sediments correlated to Rio Claro Formation. Therefore, understanding heterogeinity that characterize the aquifer and its hydraulic properties is vital to optimization and improvement of remediation process. For hydrogeological characterization of the local aquifer, a conceptual hydrogeological model was elaborated by integrating traditional investigations tools, such as geophysical methods, piezometric level monitoring, and geological descriptions in drillings and granulometric analysis to understanding of local dynamic flow, lithological distributions and hydraulic conductivity. Numerical simulation under steady-state condition using Visual Modflow, which utilizes the finite differences method were performed to test the conceived conceptual model. The measured and calculated hydraulic heads are in excellent agreement, showing the consistency of the conceptual model.

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37

Sousa, Nadson de. "Metodos de diferenças finitas : conceitos e interpretações." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306426.

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Orientador: Ricardo Caetano Azevedo Biloti
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: O presente trabalho aborda os métodos de diferenças finitas com suas propriedades e aplicações. Iniciamos com uma revisão histórica, destacando alguns matemáticos que participaram do desenvolvimento da teoria de métodos de diferenças. Em seguida, apresentamos alguns modelos matemáticos compostos por equações diferenciais. Através da equação de advecção, estudamos métodos de diferenças explícitos, com especial enfoque para as propriedades de erro de truncamento, consistência, estabilidade e convergência dando ênfase ao Teorema de Lax. Estudamos a análise de Fourier e a condição de von Neumann para interpretar a amplitude, a dissipação e a dispersão das soluções numéricas. Abordamos os métodos Upwind, de Lax-Friedrichs e de Lax-Wendroff. Por fim, exemplificamos numericamente os conceitos e propriedades estudados com comparações entre os métodos, aplicados em um problema teste.
Abstract: The present work approaches finite-difference methods, their properties, and their applications. We present a historical review, including some mathematieians who participated in the development of the theory of differences. Furthermore, we present some mathematical models consisting of differential equatiolls. Through the advection equationl, we study explicit finite-difference methods, detailing their truncation error, consistency, stability and conlvergence properties. We employ Fourier analysis and the von Neumann condition to study the amplitude, dissipation and dispersion of numerical solutions. We compare three methods: Upwind, Lax-Friedrichs and Lax-Wendroff. Finally, we perform numerical tests to illustrate the concepts and properties studied in this work.
Mestrado
Analise Numerica
Mestre em Matemática

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38

Bouwer, Abraham. "The Du Fort and Frankel finite difference scheme applied to and adapted for a class of finance problems." Diss., Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-10122009-193152.

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39

Kress, Wendy. "High Order Finite Difference Methods in Space and Time." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3559.

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40

Pezant, Joannes Charles. "High temperature thickness monitoring using ultrasonic waves." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26577.

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Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Michaels, Jennifer; Committee Member: Jacobs, Laurence; Committee Member: Michaels, Thomas. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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41

Maloney, James G. "Analysis and synthesis of transient antennas using the Finite-Difference Time-Domain (FDTD)." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/15052.

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Liow, J. (Jeih-San). "A two dimensional finite-difference simulation of seismic wave propagation in elastic media." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/25781.

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43

Kıran, Güçoğlu Arzu Tanoğlu Gamze. "The solution of some differential equations by nonstandard finite difference method/." [S.l.] : [s.n.], 2005. http://library.iyte.edu.tr/tezler/master/matematik/T000332.pdf.

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Thesis (Master)--İzmir Institute of Technology, İzmir, 2005
Keywords: Nonlinear differential equations, finite difference method, numeric simulation. Includes bibliographical references (leaves. 55-57).

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44

Wang, Bohe. "The application of finite difference method and MATLAB in engineering plates." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=1037.

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Thesis (M.S.)--West Virginia University, 1999.
Title from document title page. Document formatted into pages; contains iv, 87 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 86-87).

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45

Chavannes, Nicolas Pierre. "Local mesh refinement algorithms for enhanced modeling capabilities in the FDTD method /." Konstanz : Hartung-Gorre, 2002. http://www.loc.gov/catdir/toc/fy0801/2006483066.html.

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Tyler, Jonathan. "Analysis and implementation of high-order compact finite difference schemes /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2177.pdf.

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47

Jahnke, Gunnar. "Methods for Seismic Wave Propagation on Local and Global Scales with Finite Differences." Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-112352.

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Ciydem, Mehmet. "Ray Based Finite Difference Method For Time Domain Electromagnetics." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606633/index.pdf.

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In this study, novel Ray Based finite difference method for Time Domain electromagnetics(RBTD) has been developed. Instead of solving Maxwell&rsquo
s hyperbolic partial differential equations directly, Geometrical Optics tools (wavefronts, rays) and Taylor series have been utilized. Discontinuities of electromagnetic fields lie on wavefronts and propagate along rays. They are transported in the computational domain by transport equations which are ordinary differential equations. Then time dependent field solutions at a point are constructed by using Taylor series expansion in time whose coefficients are these transported distincontinuties. RBTD utilizes grid structure conforming to wave fronts and rays and treats all electromagnetic problems, regardless of their dimensions, as one dimensional problem along the rays. Hence CFL stability condition is implemented always at one dimensional eqaulity case on the ray. Accuracy of RBTD depends on the accuracy of grid generation and numerical solution of transport equations. Simulations for isotropic medium (homogeneous/inhomogeneous) have been conducted. Basic electromagnetic phenomena such as propagation, reflection and refraction have been implemented. Simulation results prove that RBTD eliminates numerical dispersion inherent to FDTD and is promising to be a novel method for computational electromagnetics.

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Lee, Hwa Ok. "Cylindrical FDTD analysis of LWD tools through anisotropic dipping layered earth media." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1146148166.

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Wagner, Christopher Lincoln. "Theoretical basis for numerically exact three-dimensional time-domain algorithms." Online access for everyone, 2004. http://www.dissertations.wsu.edu/Dissertations/Spring2004/c%5Fwagner%5F050404.pdf.

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Dissertations / Theses on the topic 'Finite differences'

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