Dissertations / Theses on the topic 'Poisson's equation'
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Xie, Wenzheng. "A sharp inequality for Poisson's equation in arbitrary domains and its applications to Burgers' equation." Thesis, University of British Columbia, 1991. http://hdl.handle.net/2429/31859.
Full textScience, Faculty of
Mathematics, Department of
Graduate
Nystrand, Thomas. "Summation By Part Methods for Poisson's Equation with Discontinuous Variable Coefficients." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-235418.
Full textMoussa, Jonathan Edward. "The Schroedinger-Poisson selfconsistency in layered quantum semiconductor structures." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-1124103-230904/.
Full textMayboroda, Svitlana. "The poisson problem on Lipschitz domains." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4133.
Full textThe entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (January 25, 2007) Vita. Includes bibliographical references.
Garcia, Hilares Nilton Alan. "A Parallel Aggregation Algorithm for Inter-Grid Transfer Operators in Algebraic Multigrid." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/94618.
Full textModeling real-world problems incurs a high computational cost because these mathematical models involve large-scale data manipulation. Thus we need fast and efficient algorithms. Nowadays there are many high-performance approaches for these problems. One such method is called the Multigrid algorithm. This approach models a physical domain using a hierarchy of grids, and so the effectiveness of these approaches relies on how well data can be transferred from grid to grid. In this thesis, we focus on the aggregation approach, which clusters a grid’s vertices according to its connections. We also provide an alternative parallel aggregation algorithm to give a faster solution. We show numerous experimental results that compare different aggregation approaches and multigrid methods, showing that our proposed algorithm performs better in serial and parallel than other popular implementations.
Geng, Weihua. "Interface method and Green's function based Poisson Boltzmann equation solver and interface technique based molecular dynamics." Diss., Connect to online resource - MSU authorized users, 2008.
Find full textPilorget, Marc. "Development of a dynamic calculation tool forsimulation of ditching." Thesis, KTH, Lättkonstruktioner, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-31695.
Full textBrenčys, Liutauras. "Puasono lygties sprendimas naudojantis šaltinio apibendrintomis hiperbolinės funkcijomis." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20110804_100133-71588.
Full textIt consists of Poisson equation solution in the "ball" potential algorithm. In this method the Poisson equation, the decision problem are reduced to linear algebraic equations system solution. Created and tested a mathematical package MATHCAD program for that decision. Compared to solutions with those obtained analytically, estimated to obtain accurate solutions. This solution can be used to calculate the real physical potentials, given the real potential of the real workloads.
Kåhlman, Niklas. "Summation By Parts Finite Difference Methods with Simultaneous Approximation Terms for the Heat Equation with Discontinuous Coefficients." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-84777.
Full textHoyles, Matthew, and Matthew Hoyles@anu edu au. "Computer Simulation of Biological Ion Channels." The Australian National University. Theoretical Physics, 2000. http://thesis.anu.edu.au./public/adt-ANU20010702.135814.
Full textApel, T., and F. Milde. "Realization and comparison of various mesh refinement strategies near edges." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800531.
Full textDi, Cosmo Jonathan. "Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209863.
Full textIn this thesis, we have been interested in standing waves, which satisfy an elliptic partial differential equation. When this equation is seen as a singularly perturbed problem, its solutions concentrate, in the sense that they converge uniformly to zero outside some concentration set, while they remain positive on this set.
We have obtained three kind of new results. Firstly, under symmetry assumptions, we have found solutions concentrating on a sphere. Secondly, we have obtained the same type of solutions for the Schrödinger-Poisson system. The method consists in applying the mountain pass theorem to a penalized problem. Thirdly, we have proved the existence of solutions of the nonlinear Schrödinger equation concentrating at a local maximum of the potential. These solutions are found by a more general minimax principle. Our results are characterized by very weak assumptions on the potential./
L'équation de Schrödinger non-linéaire apparaît dans différents domaines de la physique, par exemple dans la théorie des condensats de Bose-Einstein ou dans des modèles de propagation d'ondes. D'un point de vue mathématique, l'étude de cette équation est intéressante et délicate, notamment parce qu'elle peut posséder un ensemble très riche de solutions avec des comportements variés.
Dans cette thèse ,nous nous sommes intéressés aux ondes stationnaires, qui satisfont une équation aux dérivées partielles elliptique. Lorsque cette équation est vue comme un problème de perturbations singulières, ses solutions se concentrent, dans le sens où elles tendent uniformément vers zéro en dehors d'un certain ensemble de concentration, tout en restant positives sur cet ensemble.
Nous avons obtenu trois types de résultats nouveaux. Premièrement, sous des hypothèses de symétrie, nous avons trouvé des solutions qui se concentrent sur une sphère. Deuxièmement, nous avons obtenu le même type de solutions pour le système de Schrödinger-Poisson. La méthode consiste à appliquer le théorème du col à un problème pénalisé. Troisièmement, nous avons démontré l'existence de solutions de l'équation de Schrödinger non-linéaire qui se concentrent en un maximum local du potentiel. Ces solutions sont obtenues par un principe de minimax plus général. Nos résultats se caractérisent par des hypothèses très faibles sur le potentiel.
Doctorat en sciences, Spécialisation mathématiques
info:eu-repo/semantics/nonPublished
Zhou, Dong. "High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/295839.
Full textPh.D.
Projection methods for the incompressible Navier-Stokes equations (NSE) are efficient, but introduce numerical boundary layers and have limited temporal accuracy due to their fractional step nature. The Pressure Poisson Equation (PPE) reformulations represent a class of methods that replace the incompressibility constraint by a Poisson equation for the pressure, with a suitable choice of the boundary condition so that the incompressibility is maintained. PPE reformulations of the NSE have important advantages: the pressure is no longer implicitly coupled to the velocity, thus can be directly recovered by solving a Poisson equation, and no numerical boundary layers are generated; arbitrary order time-stepping schemes can be used to achieve high order accuracy in time. In this thesis, we focus on numerical approaches of the PPE reformulations, in particular, the Shirokoff-Rosales (SR) PPE reformulation. Interestingly, the electric boundary conditions, i.e., the tangential and divergence boundary conditions, provided for the velocity in the SR PPE reformulation render classical nodal finite elements non-convergent. We propose two alternative methodologies, mixed finite element methods and meshfree finite differences, and demonstrate that these approaches allow for arbitrary order of accuracy both in space and in time.
Temple University--Theses
Bäck, Viktor. "Localization of Multiscale Screened Poisson Equation." Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-180928.
Full textLozano, Guadalupe I. "Poisson geometry of the Ablowitz-Ladik equations." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/290120.
Full textVogrinc, Jure. "Poisson equation and weak approximation for Metropolis-Hastings chains." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/56621.
Full textCARMO, FABIANO PETRONETTO DO. "POISSON EQUATION AND THE HELMHOLTZ-HODGE DECOMPOSITION WITH SPH OPERATORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=12140@1.
Full textFUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
A equação diferencial parcial de Poisson é de fundamental importância em várias áreas de pesquisa, dentre elas: matemática, física e engenharia. Para resolvê-la numericamente utilizam-se vários métodos, tais como os já tradicionais métodos das diferenças finitas e dos elementos finitos. Este trabalho propõe um método para resolver a equação de Poisson, utilizando uma abordagem de sistema de partículas conhecido como SPH, do inglês Smoothed Particles Hydrodynamics. O método proposto para a solução da equação de Poisson e os operadores diferenciais discretos definidos no método SPH, chamados de operadores SPH, são utilizados neste trabalho em duas aplicações: na decomposição de campos vetoriais; e na simulação numérica de escoamentos de fluidos monofásicos e bifásicos utilizando a equação de Navier-Stokes.
Poisson`s equation is of fundamental importance in many research areas in engineering and the mathematical and physical sciences. Its numerical solution uses several approaches among them finite differences and finite elements. In this work we propose a method to solve Poisson`s equation using the particle method known as SPH (Smoothed Particle Hydrodynamics). The proposed method together with an accurate analysis of the discrete differential operators defined by SPH are applied in two related situations: the Hodge-Helmholtz vector field decomposition and the numerical simulation of the Navier-Stokes equations.
Zhang, Mei. "Some problems on conservation laws and Vlasov-Poisson-Boltzmann equation /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23749465f.pdf.
Full text"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [90]-94)
Labra, Bahena Luis R. "Multilevel Solution of the Discrete Screened Poisson Equation for Graph Partitioning." Thesis, California State University, Long Beach, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10638940.
Full textA new graph partitioning algorithm which makes use of a novel objective function and seeding strategy, Product Cut, frequently outperforms standard clustering methods. The solution strategy on solving this objective depends on developing a fast solution method for the systems of graph--based analogues of the screened Poisson equation, which is a well-studied problem in the special case of structured graphs arising from PDE discretization.
In this work, we attempt to improve the powerful Algebraic Multigrid (AMG) method and build upon the recently introduced Product Cut algorithm. Specifically, we study the consequences of incorporating a dynamic determination of the diffusion parameter by introducing a prior to the objective function. This culminates in an algorithm which seems to partially eliminate an advantage present in the original Product Cut algorithm's slower implementation.
Денисов, Станіслав Іванович, Станислав Иванович Денисов, Stanislav Ivanovych Denysov, V. M. Bohopolskyi, and N. E. Shypilov. "Master Equation for a Localized Particle Driven by Poisson White Noise." Thesis, Sumy State University, 2018. http://essuir.sumdu.edu.ua/handle/123456789/67936.
Full textMakarov, Mihail. "On the second poisson structure for the Korteweg-de Vries equation /." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487949508367548.
Full textKikuchi, Hiroaki. "Existence and stability of standing waves for Schrodinger-Poisson-Slater equation." 京都大学 (Kyoto University), 2008. http://hdl.handle.net/2433/136854.
Full textHuynh, Thanh Le Ngoc. "A fast enriched FEM for Poisson equations involving interfaces." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/45278.
Full textIncludes bibliographical references (leaves 55-56).
We develop a fast enriched finite element method for solving Poisson equations involving complex geometry interfaces by using regular Cartesian grids. The presence of interfaces is accounted for by developing suitable jump conditions. The immersed boundary method (IBM) and the immersed interface method (IIM) are successfully used to solve these problems when combined with a fast Fourier transform. However, the IBM and the IIM, which are developed from the finite difference method, have several disadvantages including the characterization of the null spaces and the inability to treat complex geometries accurately. We propose a solution to these difficulties by employing the finite element method. The continuous Galerkin solution approximations at the interface elements are modified using the enriched basis functions to make sure that the optimal convergence rates are obtained. Here, the FFT is applied in the fast Poisson solver to significantly accelerate the computational processes for solving the global matrix system. With reasonably small interfaces, the operational cost is almost linearly proportional to the number of the Cartesian grid points. The method is further extended to solve problems involving multi-materials while preserving the optimal accuracy. Several benchmark examples are shown to demonstrate the performance of the method.
by Thanh Le Ngoc Huynh.
S.M.
CAMALET, EUGENE. "Methodes de couplage euler-lagrange pour les equations d'euler-poisson." Paris 6, 1995. http://www.theses.fr/1995PA066276.
Full textVecil, Francesco. "A contribution to the simulation of Vlasov-based models." Doctoral thesis, Universitat Autònoma de Barcelona, 2007. http://hdl.handle.net/10803/3100.
Full textLa BTE ha de ser acoplada con una ecuación o sistema de ecuaciones para calcular el campo de fuerza: para estructuras simples se usa la ecuación de Poisson; para plasmas, donde los efectos magnéticos no se pueden despreciar debido a las altas velocidades de las partículas, se usa la fuerza de Lorentz, por lo cual se han de resolver las ecuaciones de Maxwell; en nanoestructuras, por ejemplo transistores con dimensiones confinadas, la ecuación de Poisson necesita ser acoplada con la ecuación de Schrödinger para la descripción de las dimensiones cuánticas y para la descomposición en sub-bandas, o niveles de energía.
Las colisiones son el scattering que las cargas padecen debido a las interacciones con otras cargas o con el retículo cristalino fijo, representado en forma de fonones. En la tesis se emplean diversos operadores de scattering: los más simples son operadores lineales de relajación; se estudia un modelo para la simulación de semiconductores donde se tienen en cuenta colisiones con fonones acústicos, en aproximación elástica, y fonones ópticos.
Tras la introducción, en el primer capítulo se desarrollan los métodos numéricos más importantes: primero un método de interpolación no oscilante (PWENO), necesario para evitar las oscilaciones producidas por la reconstrucción por polinomios de Lagrange, que incrementa la variación total cuando aparecen choques: las oscilaciones en el espacio de fases son características del problema, pero si el método añade oscilaciones espúreas (es decir, debidas al método en sí), entonces el resultado numérico no tiene sentido, o simplemente explota. El segundo método numérico fundamental es la técnica de splitting: cuando se resuelve un problema complicado, si se puede dividir en sub-problemas y resolverlos por separado, entonces se puede reconstruir una aproximación para el problema completo; esta técnica se usa para el time splitting (separación de la parte de transporte y de colisión) y el splitting dimensional (dividir el espacio de fases en posición y velocidad). La tercera herramienta fundamental es un sólver para advección lineal: se usan dos métodos, uno basado en trazar hacia atrás las características a nivel puntual y otro basado en reconstruir valores integrales en segmentos en lugar de puntos; el primero controla mejor las oscilaciones, el segundo fuerza la conservación de masa.
En el capítulo 2 estos métodos se aplican a algunos tests conocidos para averiguar su solidez.
En el capítulo 3 estos métodos se aplican a la simulación de un diodo, y los resultados se comparan con resultados anteriores obtenidos por esquemas Runge-Kutta basados en diferencias finitas para aproximar las derivadas parciales.
El capítulo 4 está dedicado a la construcción y simulación de modelos intermedios entre una ecuación cinética, con operador de colisión de tipo relajación, y su aproximación más grosera, ésta última siendo la ecuación del calor. Para obtener modelos intermedios, se busca un cierre de las ecuaciones de los momentos de orden cero y uno. Se proponen esquemas "asymptotic-preserving" para la ecuación cinética, que evitan la stiffness de la parte de advección a través de una descomposición de la función de distribución en su media más fluctuaciones. En cuanto a las clausuras de las ecuaciones de los momentos, se proponen esquemas de relajación para aislar las no-linealidades. Estos métodos son aplicados a un test conocido, el Su-Olson test.
El último capítulo está dedicado a la simulación de un MOSFET (Metal Oxide Semiconductor Field Effect Transistor) 2D de dimensión nanométrica en el que los electrones se comportan como partículas en una dimensión y como ondas en las dimensiones confinadas. La descomposición en sub-bandas se realiza a través de una ecuación de Schrödinger 1D en estado estacionario. Las dimensiones, así como las sub-bandas, están acopladas por la ecuación de Poisson en la expresión de la densidad, y por el operador de colisión. Se propone un sólver microscópico para estados transitorios, basado en técnicas de splitting para las BTEs (una para cada nivel de energía), métodos de características para el transporte y una iteración de tipo Newton para resolver el problema acoplado Schrödinger-Poisson para el cálculo del campo de fuerza.
This thesis is dedicated to the development, application and test of numerical methods for the numerical simulation of problems arising from physics and electronic engineering. The main tool which is used all along the work is the Vlasov (transport) equation in the form of the Boltzmann Transport Equation (BTE) for the description of the transport and collisions of charged particles in plasmas and electronic devices: charge carriers are driven by a force field and scattered by other carriers or phonons (pseudo-particles giving an effective representation of the oscillating field produced by the vibrating ions).
The BTE must be coupled to an equation or a system of equations for the computation of the force field: for simple structures the Poisson equation is used; for plasmas, where the magnetic phenomena cannot be neglected due to the high velocities of the particles, the Lorentz force is used, so the Maxwell equations have to be solved; for nanostructures, e.g. transistors with confined dimensions, the Poisson equation needs coupling with Schrödinger equation for the description of the quantum dimensions and the decomposition into subbands, or energy levels.
Collisions mean the scattering the carriers suffer due to the interactions with other carriers or the fixed lattice, in form of phonons. All along the thesis several scattering operator are used: the simplest ones are linear relaxation-time operators; a model for the simulation of a semiconductor is studied in which collisions are taken into account with acoustic phonons, in the elastic approximation, and optical phonons.
After the introduction, in the first chapter the most important numerical methods are developed: first of all a pointwise non-oscillatory interpolation method (PWENO) needed to avoid the simple Lagrange polynomial reconstruction, which increases the total variation when shocks appear: oscillations are part of the physics of the problem, but if the method adds spurious, non-physical oscillations, then the numerical result is meaningless, or it simply blows up. The second fundamental numerical method is the splitting technique: when solving a complicated problem, if we are able to subdivide it into sub-problem and solve them for separate, then we can reconstruct an approximation for the complete problem; this technique is used for both time splitting (separate transport from collisions) and dimensional splitting (split the phase space into either dimensions). The third fundamental instrument is the solver for linear advections: two methods are used, one based on pointwise following backwards the characteristics and another one based on reconstructing integral values along segments instead of point values; the first one controls better oscillations, the second one forces mass conservation.
These methods are applied in chapter 2 to some well-known benchmark tests to control their robustness.
In chapter 3 these methods are applied to the simulation of a diode, and the results compared to previous results obtained by Runge-Kutta schemes based on finite differences schemes for the approximation of the partial derivatives.
Chapter 4 is dedicated to the construction and simulation of intermediate models between a kinetic equation, with relaxation-time collision operator, and its coarsest approximation, this one being the heat equations. In order to obtain intermediate models, the moment equations are closed at zeroth and first order. Asymptotic-preserving schemes are proposed for the kinetic equation, which avoid the stiffness of the advection part by decomposing the distribution function into its average plus fluctuations. As for the moment closures, relaxation schemes are proposed in order to confine the non-linearities in the right hand side. These methods are then applied to a known benchmark, the Su-Olson test.
The last chapter is dedicated to the simulation of a nanoscaled 2D MOSFET (Metal Oxide Field Effect Transistor) in which electrons behave as particles in one dimension and as waves in the confined dimensions. The subband decomposition is realized through a stationary-state 1D Schrödinger equation. The dimensions as well as the subbands are coupled by the Poisson equation in the expression of the density and by the collision operator. A transient-state microscopic solver is proposed, based on splitting techniques for the BTE's (one for each energy level), characteristics methods for the transport and a Newton iteration for the solution of the coupled Schrödinger-Poisson system for computing the force field.
Qiao, Zhonghua. "Numerical solution for nonlinear Poisson-Boltzmann equations and numerical simulations for spike dynamics." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/727.
Full textVasilyeva, Anna S. M. Massachusetts Institute of Technology. "A meshfree method for the Poisson equation with 3D wall-bounded flow application." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/62712.
Full textCataloged from PDF version of thesis.
Includes bibliographical references (p. 58-60).
The numerical approximation of the Poisson equation can often be found as a subproblem to many more complex computations. In the case of Lagrangian approaches of flow equations, the Poisson equation often needs to be solved on an irregular point distribution. Currently, mainly unstructured mesh-based approaches are used. Meshfree methods present a way to approximate differential operators on unstructured point clouds without the need for mesh generation. In this thesis, a 3d meshfree finite difference Poisson solver is presented. Its performance has been studies based on numerical convergence, parallel efficiency, and computational cost. Practical application of the solver is presented in a simulation of a potential flow field in a wall-bounded domain.
by Anna Vasilyeva.
S.M.
Денисов, Станіслав Іванович, Станислав Иванович Денисов, Stanislav Ivanovych Denysov, V. V. Reva, and O. O. Bondar. "Generalized Fokker-Planck Equation for the Nanoparticle Magnetic Moment Driven by Poisson White Noise." Thesis, Sumy State University, 2012. http://essuir.sumdu.edu.ua/handle/123456789/35373.
Full textKruse, Carola. "Regularity and approximation of a hyperbolic-elliptic coupled problem." Thesis, Brunel University, 2010. http://bura.brunel.ac.uk/handle/2438/5253.
Full textZhu, Douglas Xuedong. "A numerical study of incompressible Navier-Stokes equations in three-dimensional cylindrical coordinates." Connect to this title online, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1118433979.
Full textTitle from first page of PDF file. Document formatted into pages; contains xiv, 139 p.; also includes graphics (some col.) Includes bibliographical references (p. 134-139). Available online via OhioLINK's ETD Center
Colnago, Marilaine. "Um método de interface imersa de alta ordem para a resolução de equações elípticas com coeficientes descontínuos." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-24072018-104953/.
Full textElliptic interface problems are often encountered in fluid dynamics, material sciences, mechanics and other relevant fields of study. In particular, the well-known Immersed Interface Method (IIM) figures among the most effective approaches for solving non-trivial problems, where the method is traditionally used to simulate the flow behavior over complex bodies immersed in a cartesian mesh. Although their powerfulness and versatility, techniques that are built in light of the IIM impose as constraints different types of jump conditions at the interface in order to be properly managed and applicable for specific purposes. In this thesis, we introduce a novel Immersed Interface Method for solving Elliptic problems with discontinuous coefficients on cartesian grids. Different from most existing formulations that rely on various jump conditions types to get a valid solution, the present scheme reduces significatively the number of constraints when solving the PDE problem, i.e., only the ordinary jumps of the unknowns are required to be given, a priori. Our technique combines Finite Difference schemes, Ghost node strategy, correction models, and interpolation rules into a unified and concise methodology. Moreover, the method is capable of producing high-order solutions, succeeding in many practical scenarios with little available data wherein high precision is indispensable. We attest the robustness and the accuracy of the proposed method through a variety of numerical experiments involving several Elliptic problems with arbitrary interfaces. Finally, from the conducted numerical tests, we verify that the designed method produces high-order approximations from a very limited number of valid jump constraints.
Shirokoff, David (David George). "I. A pressure Poisson method for the incompressible Navier-Stokes equations : II. Long time behavior of the Klein-Gordon equations." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/68481.
Full textCataloged from PDF version of thesis.
Includes bibliographical references (p. 165-172).
In this thesis, we address two problems involving partial differential equations. In the first problem, we reformulate the incompressible Navier-Stokes equations into an equivalent pressure Poisson system. The new system allows for the recovery of the pressure in terms of the fluid velocity, and consequently is ideal for efficient but also accurate numerical computations of the Navier-Stokes equations. The system may be discretized in theory to any order in space and time, while preserving the accuracy of solutions up to the domain boundary. We also devise a second order method to solve the recast system in curved geometries immersed within a regular grid. In the second problem, we examine the long time behavior of the Klein-Gordon equation with various nonlinearities. In the first case, we show that for a positive (repulsive) strong nonlinearity, the system thermalizes into a state which exhibits characteristics of linear waves. Through the introduction of a renormalized wave basis, we show that the waves exhibit a renormalized dispersion relation and a Planck-like energy spectrum. In the second case, we discuss the case of attractive nonlinearities. In comparison, here the waves develop oscillons as long lived, spatially localized oscillating fields. With an emphasis on their cosmological implications, we investigate oscillons in an expanding universe, and study their profiles and stability. The presence of a saturation nonlinearity results in flat-topped oscillons, which are relatively stable to long wavelength perturbations.
by David Shirokoff.
Ph.D.
Hartmann, Christoph [Verfasser], and Stephan [Akademischer Betreuer] Dahlke. "The p-Poisson Equation: Regularity Analysis and Adaptive Wavelet Frame Approximation / Christoph Hartmann ; Betreuer: Stephan Dahlke." Marburg : Philipps-Universität Marburg, 2018. http://d-nb.info/1168380103/34.
Full textBailleul, Ismaël. "Frontière de Poisson d'une diffusion relativiste." Paris 11, 2006. http://www.theses.fr/2006PA112251.
Full textIn this PhD thesis, we study the asymptotic behaviour of a diffusion defined on minkowski's spacetime. The analytic counterpart of this problem is to determine the set of bounded functions belonging to the kernel of some second order differential operator. Using probabilistic methods (stochastic differential equations, coupling), one gives an explicit description of this set of functions. In the same time, one give a completely different proof of this result, in the spirit of preexisting works on random walks on groups. Besides, one shows how the geometry of spacetime reflects on the asymptotic behaviour of the diffusion. In some sense, a typical (random) trajectory eventually behaves as a light ray
Morilhat, Sylvain. "Modélisation des fluctuations de la pression pariétale d'une couche limite turbulente pour des applications en vibro-acoustique." Thesis, Toulouse, ISAE, 2018. http://www.theses.fr/2018ESAE0041/document.
Full textLarge pressure and velocity fluctuations are present inside a turbulent boundarylayer developing along a wall. A non-rigid wall can be excited by the wall pressurefluctuations and thus acoustic radiations will be emitted above and bellow the wall.This scenario is one the mechanism of intern noise generation inside aircraft. Theaim of this thesis is to elaborate a turbulent wall pressure fluctuations model inorder to compute the noise radiated by the vibrating wall at the end. Modelsdeveloped during this thesis do not rely on an semi-empirical approach as they arebased on the analytical resolution of Poisson’s equation relating pressure and velocityfluctuations. This kind of approach has already been used by Lysak and Aupoix andtheir work was the starting point of this thesis. However, their model only gives atemporal description of the wall pressure fluctuations while a temporal and spatialdescription is needed for vibro-acoustics application. The major contribution of thisthesis is to modify their model in order to overcome this incapacity. In parallelto this theoretical modelling, a wind-tunnel experimental campaign dedicated tovalidation was designed and implemented. Velocity fluctuations were measured usingLaser Doppler Velocimetry while wall pressure fluctuations were measured usingmobile wall-mounted microphones. The initial model was improved using thesemeasurements. In particular, an anisotropic description of the velocity fluctuationswas developed which is more consistent for a sheared flow than the homogeneous andisotropic description used by Lysak and Aupoix. For a large frequency range, thefinal model behaves similarly to Corcos’ model which is the most used reference forvibro-acoustics applications. However, large differences were highlighted for low andhigh frequencies. Therefore the validity of Corcos’ model is questionable for thesefrequency range. These theoretical results must still be confirmed by experimentaldata
Li, Li. "The asymptotic behavior for the Vlasov-Poisson-Boltzmann system & heliostat with spinning-elevation tracking mode /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b30082419f.pdf.
Full text"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [84]-87)
Heinrich, Bernd, and Beate Jung. "Nitsche- and Fourier-finite-element method for the Poisson equation in axisymmetric domains with re-entrant edges." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601691.
Full textHajjej, Mohamed Lasmer. "Couches initiales et limites de relaxation aux systèmes d'Euler-Poisson et d'Euler-Maxwell." Thesis, Clermont-Ferrand 2, 2012. http://www.theses.fr/2012CLF22233/document.
Full textMy work is concerned with two different systems of equations used in the mathematical modeling of semiconductors and plasmas : the Euler-Poisson system and the Euler-Maxwell system. The first is given by the Euler equations for the conservation of the mass and momentum, with a Poisson equation for the electrostatic potential. The second system describes the phenomenon of electromagnetism. It is given by the Euler equations for the conservation of the mass and momentum, with a Maxwell equations for the electric field and magnetic field which are coupled to the electron density through the Maxwell equations and act on electrons via the Lorentz force. Using an asymptotic expansion method, we study the zero relaxation limit of unipolar Euler-Poisson system and of two-fluid multidimensional Euler-Poisson equations, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimate. By employing the classical energy estimate for symmetrizable hyperbolic equations, we justify rigorously the convergence of Euler-Poisson system with well-prepared initial data. For ill-prepared initial data, the phenomenon of initial layers occurs. In this case, we also add the correction terms in the asymptotic expansion. Using an iterative method of symmetrizable hyperbolic systems and asymptotic expansion method, we study the zero-relaxation limit of unipolar and bipolar Euler-Maxwell system. For well-prepared initial data, we construct an approximate solution by an asymptotic expansion up to any order. For ill-prepared initial data, we also construct initial layer corrections in the asymptotic expansion
Unal, Bulent. "Doubly warped products /." free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9974692.
Full textRaeli, Alice. "Solution of the variable coefficients Poisson equation on Cartesian hierarchical meshes in parallel : applications to phase changing materials." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0669/document.
Full textWe consider problems governed by a linear elliptic equation with varying coéficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second order accuracy. Numerical illustrations relevant for actual applications are presented in two and three-dimensional configurations
Zhelezov, Gleb, and Gleb Zhelezov. "Coalescing Particle Systems and Applications to Nonlinear Fokker-Planck Equations." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/624562.
Full textSilva, Marline Ilha da. "Estudo de métodos multigrid para solução de equações do tipo Poisson em malhas esféricas geodésicas icosaédricas." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-09042015-160400/.
Full textThis work is dedicated to the numerical solution of elliptic equations on the sphere, discretized on geodesic icosahedral grids. Spherical meshes generated from projections of platonic solids received considerable attention in the last decade, once they are almost isotropic and do not present a concentration of grid points around the poles, as traditional latitude-longitude grids. In particular, the geodesic icosahedral spherical grids have been adopted in the development of several atmospheric models. In these models, the necessity to solve Poisson type equations is very common, providing a motivation for our present work. We have employed a discretization of the Laplace operator based on finite volumes. We write the Laplacian as the divergent of the gradient operator and use Gauss theorem to derive the discretization of the operator. We integrate the fluxes along the cell borders and approximate them through finite-differences. We first validated the discretization solving Poisson\'s equation with a simple (and very innefficient) Jacobi-Relaxation and Gauss-Seidel. We then investigated the use of multigrid type schemes for the solution of this equation. We have analysed some schemes proposed in the literature, also using an idealized Local Fourier Analysis on hexagonal (planar) grids to estimate the behaviour of the schemes on the icosaedral grids. We have implemented and tested a multigrid method, comparing the performance with different relaxation schemes and transfer operators. We have obtained a very efficient method employing V(1,1) cycles with Gauss-Seidel relaxation, and full-weighting and linear interpolation as transfer-operators.
Maral, Tugrul. "Spectral (h-p) Element Methods Approach To The Solution Of Poisson And Helmholtz Equations Using Matlab." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607945/index.pdf.
Full textCartailler, Jérôme. "Asymptotic of Poisson-Nernst-Planck equations and application to the voltage distribution in cellular micro-domains." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066297/document.
Full textIn this PhD I study how electro-diffusion within biological micro and nano-domains is affected by their shapes using the Poisson-Nernst-Planck (PNP) partial differential equations. I consider non-trivial shapes such as domains with cusp and ellipses. Our goal is to develop models, as well as mathematical tools, to study the electrical properties of micro and nano-domains, to understand better how electrical neuronal signaling is regulated at those scales. In the first part I estimate the steady-state voltage inside an electrolyte confined in a bounded domain, within which we assume an excess of positive charge. I show the mean first passage time in a charged ball depends on the surface and not on the volume. I further study a geometry composed of a ball with an attached cusp-shaped domain. I construct an asymptotic solution for the voltage in 2D and 3D and I show that to leading order expressions for the voltage in 2D and 3D are identical. Finally, I obtain similar conclusion considering an elliptical-shaped domain for which I construct an asymptotic solution for the voltage in 2D and 3D. In the second part, I model the electrical compartmentalization in dendritic spines. Based on numerical simulations, I show how spines non-cylindrical geometry leads to concentration polarization effects. I then compare my model to experimental data of microscopy imaging. I develop a deconvolution method to recover the fast voltage dynamic from the data. I estimate the neck resistance, and we found that, contrary to Ohm's law, the spine neck resistance can be inversely proportional to its radius
Kopec, Marie. "Quelques contributions à l'analyse numérique d'équations stochastiques." Electronic Thesis or Diss., Rennes, École normale supérieure, 2014. http://www.theses.fr/2014ENSR0002.
Full textThis work presents some results about behavior in long time and in finite time of numerical methods for stochastic equations.In a first part, we are considered with overdamped Langevin Stochastic Differential Equations (SDE) and Langevin SDE. We show a weak backward error analysis result for its numerical approximations defined by implicit methods. In particular, we prove that the generator associated with the numerical solution coincides with the solution of a modified Kolmogorov equation up to high order terms with respect to the stepsize. This implies that every measure of the numerical scheme is close to a modified invariant measure obtained by asymptotic expansion. Moreover, we prove that, up to negligible terms, the dynamic associated with the implicit scheme considered is exponentially mixing.In a second part, we study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure μ. We focus on the discretization in time thanks to a scheme of Euler type, and on a Finite Element discretization in space and we show that the average of regular enough test functions with respect to the (possibly non unique) invariant laws of the approximations are close to the corresponding quantity for μ.More precisely, we analyze the rate of the convergence with respect to the different discretization parameters. Finally, we are concerned with semilinear SPDEs with additive space-time white noise, which the nonlinear term is a polynomial function. We analyze the rate of the weak convergence for discretization in time with an implicit splitting method
Bossa, Guilherme Volpe [UNESP]. "Determinação do grau de ionização de aminoácidos polares carregados." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/87535.
Full textFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Proteínas e peptídeos são constituídos por subunidades estruturalmente mais imples chamadas aminoácidos. Uma importante propriedade destes é que, dependendo das características do meio (tais como pH e concentração iônica), os seus grupos onizáveis podem ceder prótons e, assim, adquirir carga elétrica não nula. Tal carga nfluenciará na eficiência da formação de ligações peptídicas e em interações proteína- igante, por exemplo. Partindo da hipótese de que a diferença entre os valores de pK dos rupos ionizáveis isolados e destes como partes constituintes de um aminoácido é devida, principalmente, à interação eletrostática adicional que se atribui à presença de rupos vizinhos, elaborou-se um modelo que emprega a forma linearizada da equação de Poisson-Boltzmann para o estudo de propriedades físico-químicas de moléculas com rês grupos ionizáveis. Neste trabalho tal modelo foi aplicado aos aminoácidos: Aspartato, Glutamato, Cisteína, Tirosina, Arginina, Lisina e Histidina. Calcularam-se os valores de pK e as respectivas cargas elétricas médias de tais moléculas. Como os esultados obtidos concordaram com aqueles oriundos de trabalhos experimentais, o modelo teórico foi expandido para tratar de di, tetra, pentapeptídeos e de resíduos de isina e glutamato da proteína Staphylococcal Nuclease. Os valores do Fator de Correlação de Pearson calculados para ambos proteínas e peptídeos são superiores a 0,99, fato este que evidencia a eficiência e versatilidade do modelo ao reproduzir alores de pK reportados por outros autores
Proteins and peptides are composed of subunits structurally simpler called amino acids. An important property of these is that, depending on the medium characteristics (such pH and ionic concentration), its ionizable groups may provide protons and thereby acquire a nonzero electric charge. Such charge will affect the formation of peptide bond and protein-ligand interactions, for example. Assuming that the difference between pK values of the isolates ionizable groups and of these as constituents parts of an amino acid is mainly due to the extra electrostatic interaction attributed to the presence of neighboring groups, was developed a structure-based model that employs the linearized form of the Poisson-Boltzmann equation for the study of physicochemical properties of molecules with three ionizable groups. In this work it was applied to the amino acids: aspartate, glutamate, cysteine, tyrosine, arginine, lysine and histidine. The pK values and respective mean electric charges were calculated. As the calculated values agreed with those from experimental studies, the theoretical model has been expanded to the treatment of di, tetra, pentapeptides and Staphylococcal Nuclease residues. The Pearson Correlation Factor calculated for both proteins and peptides are above 0.99, what points to the effectiveness and versatility of the model to reproduce pK values reported by other works
Bossa, Guilherme Volpe. "Determinação do grau de ionização de aminoácidos polares carregados /." São José do Rio Preto, 2013. http://hdl.handle.net/11449/87535.
Full textOrientador: Elso Drigo Filho
Coorientador: Tereza Pereira de Souza
Banca: Iolanda Midea Cuccovia
Banca: Marcelo Andres Fossey
Resumo: Proteínas e peptídeos são constituídos por subunidades estruturalmente mais imples chamadas aminoácidos. Uma importante propriedade destes é que, dependendo das características do meio (tais como pH e concentração iônica), os seus grupos onizáveis podem ceder prótons e, assim, adquirir carga elétrica não nula. Tal carga nfluenciará na eficiência da formação de ligações peptídicas e em interações proteína- igante, por exemplo. Partindo da hipótese de que a diferença entre os valores de pK dos rupos ionizáveis isolados e destes como partes constituintes de um aminoácido é devida, principalmente, à interação eletrostática adicional que se atribui à presença de rupos vizinhos, elaborou-se um modelo que emprega a forma linearizada da equação de Poisson-Boltzmann para o estudo de propriedades físico-químicas de moléculas com rês grupos ionizáveis. Neste trabalho tal modelo foi aplicado aos aminoácidos: Aspartato, Glutamato, Cisteína, Tirosina, Arginina, Lisina e Histidina. Calcularam-se os valores de pK e as respectivas cargas elétricas médias de tais moléculas. Como os esultados obtidos concordaram com aqueles oriundos de trabalhos experimentais, o modelo teórico foi expandido para tratar de di, tetra, pentapeptídeos e de resíduos de isina e glutamato da proteína Staphylococcal Nuclease. Os valores do Fator de Correlação de Pearson calculados para ambos proteínas e peptídeos são superiores a 0,99, fato este que evidencia a eficiência e versatilidade do modelo ao reproduzir alores de pK reportados por outros autores
Abstract: Proteins and peptides are composed of subunits structurally simpler called amino acids. An important property of these is that, depending on the medium characteristics (such pH and ionic concentration), its ionizable groups may provide protons and thereby acquire a nonzero electric charge. Such charge will affect the formation of peptide bond and protein-ligand interactions, for example. Assuming that the difference between pK values of the isolates ionizable groups and of these as constituents parts of an amino acid is mainly due to the extra electrostatic interaction attributed to the presence of neighboring groups, was developed a structure-based model that employs the linearized form of the Poisson-Boltzmann equation for the study of physicochemical properties of molecules with three ionizable groups. In this work it was applied to the amino acids: aspartate, glutamate, cysteine, tyrosine, arginine, lysine and histidine. The pK values and respective mean electric charges were calculated. As the calculated values agreed with those from experimental studies, the theoretical model has been expanded to the treatment of di, tetra, pentapeptides and Staphylococcal Nuclease residues. The Pearson Correlation Factor calculated for both proteins and peptides are above 0.99, what points to the effectiveness and versatility of the model to reproduce pK values reported by other works
Mestre
Plewa, Joseph-Marie. "Simulation 3D d'une décharge couronne pointe-plan, dans l'air : calcul haute performance, algorithmes de résolution de l'équation de Poisson et analyses physiques." Thesis, Toulouse 3, 2017. http://www.theses.fr/2017TOU30184/document.
Full textThis work is devoted to the three dimensional (3D) simulation of streamer corona discharges in air at atmospheric pressure using high-performance parallel computing. When a pulsed high-voltage is applied between a tip and a plane in air, the strong electric field lines constricted around the tip induce the simultaneous propagation of several streamers leading to a corona discharge with a tree structure. Only a true 3D electro-hydrodynamics simulation is able to reproduce this branching and to provide the orders of magnitude of the local deposited energy and the concentration of the species created during the discharge phase. However, such a 3D simulation which requires large computational memory and huge time calculation is nowadays accessible only when performed with massively parallel computation. In the field of 3D electro-hydrodynamics simulations, a special attention must be paid to the efficiency of solvers in solving 3D elliptic equations because their contribution can exceed 80% of the global computation time. Therefore, a specific chapter is devoted to test the performance of iterative and direct methods (such as SOR R&B, BiCGSTAB and MUMPS) in solving elliptic equations, using the massively parallel computation and the MPI library. The calculations are performed on the supercomputer EOS of the CALMIP network, with a number of computing cores and meshes increasing up to respectively 1800 and 8003 (i.e. more than 1/2 Billion meshes). The performances are compared for the calculation of the geometric potential and in a dynamic simulation conditions consisting in the propagation of an analytical space charge density characteristic of the streamers. To perform a complete 3D simulation of the streamer discharge, must also involve a robust algorithm able to solve the coupled conservation equations of the charged particle density with very sharp gradients characteristic of the streamers. In this manuscript, the MUSCL algorithm is tested under different propagation conditions of a cubic density (with uniform or non-uniform velocity field). The 3D code, designed to solve the complete electro-hydrodynamics model of the discharge (coupling the conservation equations, the Poisson equation and the chemical kinetics) is validated by comparing the 3D and 2D results in a simulation conditions presenting a rotational symmetry around the propagation axis of a mono-filamentary streamer. Finally, the first results of the 3D simulations of the discharge phase with the propagation of one or several asymmetric streamers are presented and analyzed. These simulations allow to follow the tree structure of a corona discharge when a pulsed voltage is applied between a tip and a plane. The ignition of the tree structure is studied as a function of the initial position of the plasma spots
SALANON, BRUNO. "Stabilite des solutions des equations de transport application a la resolution numerique du systeme de vlasov-poisson." Nice, 1997. http://www.theses.fr/1997NICE5085.
Full textYE, TAI-KUN, and 葉泰昆. "Three-dimensional grid generation using poisson's equation." Thesis, 1992. http://ndltd.ncl.edu.tw/handle/13488787968830010784.
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