Dissertationen zum Thema „Analyse numérique des équations aux dérivées partielles“
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Merlet, Benoît. „Sur quelques équations aux dérivées partielles et leur analyse numérique“. Paris 11, 2004. http://www.theses.fr/2004PA112162.
Der volle Inhalt der QuelleIn this thesis, four Partial Differential Equations of different nature are studied, numerically or/and theoretically. The first part deals with non-conservative hyperbolic systems in one space dimension. In the case of non-conservative hyperbolic systems, several definitions of shock waves exist in the literature, in this paper, we propose and study a new, very simple one in the case of genuinely non-linear fields. The second part is concerned with the Harmonic Map flow. We build solutions to the harmonic map flow from the unit disk into the unit sphere which have constant degree, in a co-rotational symmetric frame. First we prove the existence of such solutions, using a time semi-discrete scheme then we compute numerically these solutions by a moving-mesh method which allows us to deal with the singularities. The third part deals with the initial-and-boundary value problem for the Kadomtse-Petviashvili II equation posed on a strip with a Dirichlet left boundary condition and two kinds of conditions on the right boundary. Moreover we treat the case of the half plane and we show a result of convergence. In the last part, we investigate by numerical means a conjecture proposed by Guy David about the existence of a new Global Minimizer for the Mumford-Shah Functional in R^3. We are led to study a spectral problem for the Laplace operator with Neumann boundary conditions on a two dimensional subdomain of the sphere S^2 with reentrant corners. In particular, we have to compute the first eigenvector of this operator and accurate approximations of the singular coefficients of this eigenvector at each corner. For that we use the Singular Complement Method
Ponenti, Pierre-Jean. „Algorithmes en ondelettes pour la résolution d'équations aux dérivées partielles“. Aix-Marseille 1, 1994. http://www.theses.fr/1994AIX11082.
Der volle Inhalt der QuelleLeboucher, Guillaume. „Méthodes de moyennisation stroboscopique appliquées aux équations aux dérivées partielles hautement oscillantes“. Thesis, Rennes 1, 2015. http://www.theses.fr/2015REN1S121/document.
Der volle Inhalt der QuelleThis thesis presents some original work in the field of high order averaging procedure. In particular, we are interested in stroboscopic and quasi-stroboscopic averaging procedure in abstract Banach or Hilbert spaces. This procedures is applied to concrete examples: some highly oscillatory evolution equations. More precisely, we first show a theorem of stroboscopic averaging in a Banach space where we obtain exponential error estimates. This theorem is then applied on two semi-linear and highly oscillatory wave equations. We also put in evidence that the {\it Stroboscopic Averaging Method} works fine with a semi-linear wave equation with Dirichlet conditions. Finally, the averaging procedure puts in evidence, numerically, an interesting dynamics regarding the semi-linear wave equation with Dirichlet conditions. In a second part, we present a quasi-stroboscopic averaging theorem in a Hilbert space with exponential error estimates. This theorem is applied on a semi-linear Schrödinger equation. This equation has first, to be project in a finite dimensional space in order to fit in the hypotheses of the theorem. We then write a quasi-stroboscopic averaging theorem for a semi-linear Schrödinger equation with polynomial error estimates
Duminil, Sébastien. „Extrapolation vectorielle et applications aux équations aux dérivées partielles“. Phd thesis, Université du Littoral Côte d'Opale, 2012. http://tel.archives-ouvertes.fr/tel-00790115.
Der volle Inhalt der QuelleMonthe, Luc Arthur. „Etude des équations aux dérivées partielles hyperboliques application aux équations de Saint-Venant“. Rouen, 1997. http://www.theses.fr/1997ROUES074.
Der volle Inhalt der QuelleAghili, Joubine. „Résolution numérique d'équations aux dérivées partielles à coefficients variables“. Thesis, Montpellier, 2016. http://www.theses.fr/2016MONTT250/document.
Der volle Inhalt der QuelleThis Ph.D. thesis deals with different aspects of the numerical resolution of Partial Differential Equations.The first chapter focuses on the Mixed High-Order method (MHO). It is a last generation mixed scheme capable of arbitrary order approximations on general meshes. The main result of this chapter is the equivalence between the MHO method and a Hybrid High-Order (HHO) primal method.In the second chapter, we apply the MHO/HHO method to problems in fluid mechanics. We first address the Stokes problem, for which a novel inf-sup stable, arbitrary-order discretization on general meshes is obtained. Optimal error estimates in both energy- and L2-norms are proved. Next, an extension to the Oseen problem is considered, for which we prove an error estimate in the energy norm where the dependence on the local Péclet number is explicitly tracked.In the third chapter, we analyse a hp version of the HHO method applied to the Darcy problem. The resulting scheme enables the use of general meshes, as well as varying polynomial orders on each face.The dependence with respect to the local anisotropy of the diffusion coefficient is explicitly tracked in both the energy- and L2-norms error estimates.In the fourth and last chapter, we address a perspective topic linked to model order reduction of diffusion problems with a parametric dependence. Our goal is in this case to understand the impact of the choice of the variational formulation (primal or mixed) used for the projection on the reduced space on the quality of the reduced model
Siaud, Bernard. „Etude de la résolution des équations aux dérivées partielles en 3D sur des machines parallèles“. Ecully, Ecole centrale de Lyon, 1995. http://www.theses.fr/1995ECDL0019.
Der volle Inhalt der QuelleA comparative study of different parallel computers have been realised from a algorithm solving a system of partial derivative equations (PDE). This work permitted to a evaluate the influence of parallelism on the time of calculation and the time of communication interprocessor. On this basis, we could define more precisely the shedule of conditions of the computer HA3D for intended to solve PDE's. Simple algorithms have been developped to improve convergence of Gauss-Seidel method (to decrease the number of calcultations) : approximation by big mailing, variation of coefficient of subrelaxation (VCS). The first method consist of initialisation of variable values (physical size to establish) by a calcul on more rough mailings of the studied domain discretized by methods of volums or differences finit. The VCS method is used a the time of updating of coefficients to take variable dependency into account
TUOMELA, JUKKA. „Analyse de certains problèmes liés a la résolution numérique des équations aux dérivées partielles hyperboliques linéaires“. Paris 7, 1992. http://www.theses.fr/1992PA077200.
Der volle Inhalt der QuelleTlili, Abderaouf. „Analyse de quelques méthodes numériques pour des problèmes d'évolution“. Lyon 1, 1994. http://www.theses.fr/1994LYO10293.
Der volle Inhalt der QuelleMartel, Sofiane. „Theoretical and numerical analysis of invariant measures of viscous stochastic scalar conservation laws“. Thesis, Paris Est, 2019. http://www.theses.fr/2019PESC1040.
Der volle Inhalt der QuelleThis devoted to the theoretical and numerical analysis of a certain class of stochastic partial differential equations (SPDEs), namely scalar conservation laws with viscosity and with a stochastic forcing which is an additive white noise in time. A particular case of interest is the stochastic Burgers equation, which is motivated by turbulence theory. We focus on the long time behaviour of the solutions of these equations through a study of the invariant measures. The theoretical part of the thesis constitutes the second chapter. In this chapter, we prove the existence and uniqueness of a solution in a strong sense. To this end, estimates on Sobolev norms up to the second order are established. In the second part of Chapter~2, we show that the solution of the SPDE admits a unique invariant measure. In the third chapter, we aim to approximate numerically this invariant measure. For this purpose, we introduce a numerical scheme whose spatial discretisation is of the finite volume type and whose temporal discretisation is a split-step backward Euler method. It is shown that this kind of scheme preserves some fundamental properties of the SPDE such as energy dissipation and L^1-contraction. Those properties ensure the existence and uniqueness of an invariant measure for the numerical scheme. Thanks to a few regularity estimates, we show that this discrete invariant measure converges, as the space and time steps tend to zero, towards the unique invariant measure for the SPDE in the sense of the second order Wasserstein distance. Finally, numerical experiments are performed on the Burgers equation in order to illustrate this convergence as well as some small-scale properties related to turbulence
Benjelloun, Saad. „Quelques problèmes d’écoulements multi-fluide : analyse mathématique, modélisation numérique et simulation“. Thesis, Cachan, Ecole normale supérieure, 2012. http://www.theses.fr/2012DENS0074/document.
Der volle Inhalt der QuelleThis thesis contains three independent parts.The first part presents a proof of existence of weak global solutions to a Vlasov-incompressible-Navier-Stokes system with variable density. This system is obtained formally from a classical Vlasov-incompressible-Navier-Stokes model with fragmentation for which only two values for the particules radii are considered: a radius r1 for non fragmented particules and a radius r2<
Baccou, Jean. „Analyses multirésolutions et problèmes de bord : applications au traitement d'images et à la résolution numérique d'équations aux dérivées partielles“. Aix-Marseille 1, 2004. http://www.theses.fr/2004AIX11061.
Der volle Inhalt der QuelleAzerad, Pascal. „Contributions à l'étude de quelques équations aux dérivées partielles, en mécanique des fluides et en génie côtier“. Habilitation à diriger des recherches, Université Montpellier II - Sciences et Techniques du Languedoc, 2007. http://tel.archives-ouvertes.fr/tel-00221442.
Der volle Inhalt der QuelleIls se classent en trois thèmes:
Analyse asymptotique des équations de Navier-Stokes,
Optimisation de forme d'ouvrages de lutte contre l'érosion du littoral,
Etude d'équations aux dérivées partielles comportant des termes non-locaux.
Dans le thème 1, je développe la justification mathématique de l'approximation hydrostatique pour les fluides géophysiques à faible quotient d'aspect, hypothèse couramment vérifiée en océanographie et en météorologie. C'est un problème de perturbation singulière. Je présente également l'étude théorique et numérique de l'écoulement cône-plan, utilisé en hématologie-hémostase pour le sang de patients. Il s'agit d'un problème de couche limite singulière.
Le thème 2 concerne le génie côtier. Les ouvrages utilisés tels que épis, brise-lames, enrochements sont de forme trop rudimentaire. Leur efficacité peut être améliorée significativement si leur forme est optimisée pour réduire l'énergie dissipée par la houle dans la zone proche-littorale. Nous optimisons aussi la forme de géotextiles immergés. Ce travail, réalisé dans le cadre de la thèse de Damien Isèbe, a reçu le soutien de l'ANR (projet COPTER) et s'effectue en partenariat avec le laboratoire Géosciences Montpellier et l'entreprise Bas-Rhône-Languedoc ingénierie (Nîmes).
Dans le thème 3, nous prouvons existence, unicité et régularité de solutions pour l'équation de la chaleur fractionnaire, perturbée par un bruit blanc. C'est une équation aux dérivées partielles stochastique.Nous prouvons enfin un résultat d'existence, unicité et dépendance continue pour une loi de conservation non linéaire, comportant un terme non local, qui modélise l'évolution d'un profil de dune immergée.
L'intérêt mathématique est que l'équation ne vérifie pas le principe du maximum mais possède néanmoins un effet régularisant.
Torri, Vincent. „Etude de systèmes d'équations aux dérivées partielles intervenant en physico-chimie et en optique“. Bordeaux 1, 2003. http://www.theses.fr/2003BOR12685.
Der volle Inhalt der QuelleThis work is divided into two parts : the first one is devoted to the mathematical study of a lamellar lyotrop phase under shear stress. This lamellar phase is created by adding a large quantity of surfactants in water and is submitted to a shear stress. At some shear velocity, structures called spherulits, or "onions", are created. When the shear stress is large enoug, the onion phase disappears and we observe a restabilization process, des cribed by a mathematical model. We study rigorously this last behavior and we show an instability result. A numerical analysis shows that a Hopf bifurcation occurs at some shear velocity. The second part deals with a numerical scheme which solves the 2-levels Maxwell-Bloch equations. We want to describe the evolution of oscillating solutions which propagate in long times (diffractive optics). We use WKB method and profiles to highly decrease the time-space meshes and performances are highly improved, compared to oher classical finite-difference methods like the Yee scheme
Moitier, Zoïs. „Étude mathématique et numérique des résonances dans une micro-cavité optique“. Thesis, Rennes 1, 2019. http://www.theses.fr/2019REN1S053/document.
Der volle Inhalt der QuelleThis thesis is devoted to the study of resonance frequencies of bidimensional optical cavities. More specifically, we are interested in whispering-gallery modes (modes localized along the cavity boundary with a large number of oscillations). The first part deals with the numerical computation of resonances by the finite element method using perfectly matched layers, and with a sensibility analysis in the three following situations: an unidimensional problem, a reduction of the rotationally invariant bidimensional case, and the general case. The second part focuses on the construction of asymptotic expansions of whispering-gallery modes as the number of oscillations along of boundary goes to infinity. We start by considering the case of a rotationally invariant problem for which the number of oscillations can be interpreted as a semiclassical parameter by means of an angular Fourier transform. Next, for the general case, the construction uses a phase-amplitude ansatz of WKB type which leads to a generalized Schrödinger operator. Finally, the numerically computed resonances obtained in the first part are compared to the asymptotic expansions made explicit by the use of a computer algebra software
Carcenac, Manuel. „Structures de données arborescentes et évaluation paresseuse : une nouvelle approche pour la résolution des équations aux dérivées partielles“. Toulouse, ENSAE, 1994. http://www.theses.fr/1994ESAE0008.
Der volle Inhalt der QuelleClarotto, Lucia. „Spatio-temporal prediction by stochastic partial differential equationsPrédiction spatio-temporelle par équations aux dérivées partielles stochastiques“. Electronic Thesis or Diss., Université Paris sciences et lettres, 2023. http://www.theses.fr/2023UPSLM022.
Der volle Inhalt der QuelleIn the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest. Large space-time datasets call for new numerical methods to efficiently process them. The Stochastic Partial Differential Equation (SPDE) approach has proven to be effective for the estimation and the prediction in a spatial context. We present here the unsteady advection-diffusion SPDE which defines a large class of nonseparable spatio-temporal models. A Gaussian Markov random field approximation of the solution to the SPDE is built by discretizing the temporal derivative with a finite difference method (implicit Euler) and by solving the spatial SPDE with a finite element method (continuous Galerkin) at each time step. The Streamline Diffusion stabilization technique is introduced when the advection term dominates the diffusion. Computationally efficient methods are proposed to estimate the parameters of the SPDE and to predict the spatio-temporal field by kriging, as well as to perform conditional simulations. The approach is applied to solar radiation and wind speed datasets. Its advantages and limitations are discussed, and new perspectives for future work are envisaged, especially involving a nonstationary extension of the approach. As a further contribution of the PhD, the nonseparable generalization of the Gneiting class of multivariate space-time covariance functions is presented. The main potential of the approach is the possibility to obtain entirely nonseparable models in a multivariate setting, and this advantage is shown on a weather trivariate dataset. Finally, a review of some methods for approximate estimation and prediction for spatial and spatio-temporal data is proposed, motivated by the objective of reaching a trade-off between statistical efficiency and computational complexity. These methods proved to be effective for parameter estimation and prediction in the context of the "Spatial Statistics Competition for Large Datasets" organized by the King Abdullah University of Science and Technology (KAUST) in 2021 and 2022. Lastly, possible further research directions are discussed
Hached, Mustapha. „Méthodes de sous-espaces de Krylov matriciels appliquées aux équations aux dérivées partielles“. Phd thesis, Université du Littoral Côte d'Opale, 2012. http://tel.archives-ouvertes.fr/tel-00919796.
Der volle Inhalt der QuelleBensouda, Fatima-Zohra. „Etude de la réactivité de suies Diesel à partir de mesures thermogravimétriques : résolution mathématique des équations correspondantes“. Mulhouse, 2000. http://www.theses.fr/2000MULH0559.
Der volle Inhalt der QuelleCourtès, Clémentine. „Analyse numérique de systèmes hyperboliques-dispersifs“. Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS467/document.
Der volle Inhalt der QuelleThe aim of this thesis is to study some hyperbolic-dispersive partial differential equations. A significant part is devoted to the numerical analysis and more precisely to the convergence of some finite difference schemes for the Korteweg-de Vries equation and abcd systems of Boussinesq. The numerical study follows the classical steps of consistency and stability. The main idea is to transpose at the discrete level the weak-strong stability property for hyperbolic conservation laws. We determine the convergence rate and we quantify it according to the Sobolev regularity of the initial datum. If necessary, we regularize the initial datum for the consistency estimates to be always valid. An optimization step is thus necessary between this regularization and the convergence rate of the scheme. A second part is devoted to the existence of traveling waves for the Korteweg-de Vries-Kuramoto-Sivashinsky equation. By classical methods of dynamical systems : extended systems, Lyapunov function, Melnikov integral, for instance, we prove the existence of oscillating small amplitude traveling waves
Martinez, Miguel. „Interprétations probabilistes d'opérateurs sous forme divergence et analyse de méthodes numériques probabilistes associées“. Aix-Marseille 1, 2004. http://www.theses.fr/2004AIX11068.
Der volle Inhalt der QuelleCherif, Mohamed Amine. „Sur l'approximation rationnelle pour le semi-groupe de transport“. Poitiers, 2010. http://theses.edel.univ-poitiers.fr/2010/Cherif-Mohamed-Amine/2010-Cherif-Mohamed-Amine-These.pdf.
Der volle Inhalt der QuelleIn this thesis we mix the rational approximation procedure, which is a time approximation with approximation in the sense of Kato, which is a space approximation for neutron transport equation. We apply this procedure for explicit and implicit Euler, Crank-Nicolson and Predictor-Corrector schemes which have the rate 1,2 and 3 in the sense of rational approximation. By using Cherno's Theorem, we prove the convergence and we construct also the numerical illustration for justifying the above rate of convergence. In the last chapter, we give some generalization of Schauder and Krasnoselskii fixed point theorems in Dunford-Pettis Frechet spaces and which based on the notion of weakly compactness and U-equicontraction
Zhang, Kun. „Contrôle de l'évolution d'un procédé de cristallisation en batch gouverné par des équations aux dérivées partielles“. Phd thesis, Université Claude Bernard - Lyon I, 2011. http://tel.archives-ouvertes.fr/tel-00965757.
Der volle Inhalt der QuelleRicaud, Jean-Marc (1971. „Etude d'une classe d'inéquations d'évolution implicites et application à des problèmes dynamiques de contact avec frottement“. Aix-Marseille 1, 1999. http://www.theses.fr/1999AIX11062.
Der volle Inhalt der QuelleLepage, François. „Génération de maillages tridimensionnels pour la simulation des phénomènes physiques en géosciences“. Vandoeuvre-les-Nancy, INPL, 2003. http://www.theses.fr/2003INPL072N.
Der volle Inhalt der QuelleThree-dimensional meshes are widely used in Geosciences for discretizing the geological objects of the problem domain, thus providing a support for the numerical simulation of various processes depending on physical properties, such as balanced unfolding, ray-tracing, or fluid flow modelling in porous and permeable rock bodies. However, to ensure accuracy, efficiency, and stability, mesh elements must meet several requirements, especially on their shape and size
Macherey, Arthur. „Approximation et réduction de modèle pour les équations aux dérivées partielles avec interprétation probabiliste“. Thesis, Ecole centrale de Nantes, 2021. http://www.theses.fr/2021ECDN0026.
Der volle Inhalt der QuelleIn this thesis, we are interested in the numerical solution of models governed by partial differential equations that admit a probabilistic interpretation. In a first part, we consider partial differential equations in high dimension. Based on a probabilistic interpretation of the solution which allows to obtain pointwise evaluations of the solution using Monte-Carlo methods, we propose an algorithm combining an adaptive interpolation method and a variance reduction method to approximate the global solution. In a second part, we focus on reduced basis methods for parametric partial differential equations. We propose two greedy algorithms based on a probabilistic interpretation of the error. We also propose a discrete optimization algorithm probably approximately correct in relative precision which allows us, for these two greedy algorithms, to judiciously select a snapshot to add to the reduced basis based on the probabilistic representation of the approximation error
Charrier, Julia. „Analyse numérique d’équations aux dérivées aléatoires, applications à l’hydrogéologie“. Thesis, Cachan, Ecole normale supérieure, 2011. http://www.theses.fr/2011DENS0030/document.
Der volle Inhalt der QuelleThis work presents some results about probabilistic and deterministic numerical methods for partial differential equations with stochastic coefficients, with applications to hydrogeology. We first consider the steady flow equation in porous media with a homogeneous lognormal permeability coefficient, including the case of a low regularity covariance function. We establish error estimates, both in strong and weak senses, of the error in the solution resulting from the truncature of the Karhunen-Loève expansion of the coefficient. Then we establish finite element error estimates, from which we deduce an extension of the existing error estimate for the stochastic collocation method along with an error estimate for a multilevel Monte-Carlo method. We finally consider the coupling of the previous flow equation with an advection-diffusion equation, in the case when the uncertainty is important and the correlation length is small. We propose the numerical analysis of a numerical method, which aims at computing the mean velocity of the expansion of a pollutant. The method consists in a Monte-Carlo method, combining a finite element method for the flow equation and an Euler scheme for the stochastic differential equation associated to the advection-diffusion equation, seen as a Fokker-Planck equation
Benjelloun, Saad. „Quelques problèmes d'écoulements multi-fluide : analyse mathématique, modélisation numérique et simulation“. Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00823095.
Der volle Inhalt der QuelleLa première partie présente une preuve d'existence de solutions faibles globales pour un modèle de sprays de type Vlasov-Navier-Stokes-incompressible avec densité variable. Ce modèle est obtenu par une limite formelle à partir d'un modèle Vlasov-Navier-Stokes-incompressible avec fragmentation, où seules deux valeurs de rayons de particules sont considérées : un rayon r1 pour les particules avant fragmentation, et un rayon r2<
Poncet, Romain. „Méthodes numériques pour la simulation d'équations aux dérivées partielles stochastiques non-linéaires en condensation de Bose-Einstein“. Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX069/document.
Der volle Inhalt der QuelleThis thesis is devoted to the numerical study of two stochastic models arising in Bose-Einstein condensation physics. They constitute two generalisations of the Gross-Pitaevskii Equation. This deterministic partial differential equation model the wave function dynamics of a Bose-Einstein condensate trapped in an external confining potential. The first chapter contains a simple presentation of the Bose-Einstein condensation phenomenon and of the experimental methods used to construct such systems.The first model considered enables to model the fluctuations of the confining potential intensity, and takes the form of a stochastic partial differential equation. In practice, these fluctuations lead to heating of the condensate and possibly to its collapse. In the second chapter we propose to build a numerical scheme to solve this model. It is based on a spectral space discretisation and a Crank-Nicolson discretisation in space. We show that the proposed scheme converges strongly at order at least one in probability. We also present numerical simulations to illustrate this result. The third chapter is devoted to the numerical and theoretical study of the dynamics of a stationary solution (for the deterministic equation) of vortex type. We study the influence of random disturbances of the confining potential on the solution. We show that the disturbed solution conserves the symmetries of the stationary solution for times up to at least the square of the inverse of the fluctuations intensity. These results are illustrated with numerical simulations based on a Monte-Carlo method suited to rare events estimation.The second model can be used to model the effects of the temperature on the dynamics of a Bose-Einstein condensate. In the case of finite temperature, the Bose-Einstein condensation is not complete and the condensate interacts with the non-condensed particles. These interactions are interesting to understand the dynamics of the phase transition and analyse the phenomena of symmetry breaking associated, like the spontaneous nucleation of vortices We have studied in the fourth and the fifth chapters some questions linked to the long time simulation of this model solutions. The fourth chapter is devoted to the construction of an unbiased sampling method of measures known up to a multiplicative constant. The distinctive feature of this Markov-Chain Monte-Carlo algorithm is that it enables to perform an unbiased non-reversible sampling based on an overdamped Langevin equation. It constitutes a generalization of the Metropolis-Adjusted Langevin Algorithm (MALA). The fifth chapter is devoted to the numerical study of metastable dynamics linked to the nucleation of vortices in rotating Bose-Einstein condensates. A numerical integrator and a suited Monte-Carlo methods for the simulation of metastable dynamics are proposed. This Monte-Carlo method is based on the Adaptive Multilevel Splitting (AMS) algorithm
Crouseilles, Nicolas. „Modèles cinétiques et hybrides fluide-cinétique pour les gaz et les plasmas hors équilibre“. Toulouse, INSA, 2004. http://www.theses.fr/2004ISAT0020.
Der volle Inhalt der QuelleIn this thesis, we are interested in the modeling and the numerical study of nonequilibrium gas and plasmas. To describe such systems, two ways are usually used : the fluid description and the kinetic description. When we study a nonequilibrium system, fluid models are not sufficient and a kinetic description have to be used. However, solving a kinetic model requires the discretization of a large number of variables, which is quite expensive from a numerical point of view. The aim of this work is to propose a hybrid kinetic-fluid model thanks to a domain decomposition method in the velocity space. The derivation of the hybrid model is done in two different contexts : the rarefied gas context and the more complicated plasmas context. The derivation partly relies on Levermore's entropy minimization approach. The so-obtained model is then discretized and validated on various numerical test cases. In a second stage, a numerical study of a fully kinetic model is presented. A collisional plasma constituted of electrons and ions is considered through the Vlasov-Poisson-Fokker- Planck-Landau equation. Then, a numerical scheme which preserves total mass and total energy is presented. This discretization permits in particular a numerical study of the Landau damping
Doursat, Christophe. „Qualités, défauts et améliorations des maillages algébriques et elliptiques“. Paris 6, 1994. http://www.theses.fr/1994PA066103.
Der volle Inhalt der QuelleVallaghé, Sylvain. „EEG and MEG forward modelling : computation and calibration“. Nice, 2009. http://www.theses.fr/2008NICE4095.
Der volle Inhalt der QuelleThis thesis focuses on the forward problem of electroencephalography (EEG) and magnetoencephalography (MEG). The first part deals with the calculation of the forward problem solution. We present a new finite element method (FEM) based on a regular hexahedral mesh and implicit descriptions of the domain, which allows to solve the forward problem in realistic geometries with a low computational cost. We add to this method some general reciprocal equations, derived by the adjoint method, in aim to efficiently compute the lead field of all kinds of EEG and MEG sensors. The second part is concerned with the choice of the electrical conductivities in the EEG head models. We first perform a global sensitivity analysis of the EEG topographies with respect to the conductivities for some classical head models with three or four layers. Following the results of this analysis, we then propose a method for conductivity calibration using somatosensory evoked potentials
Chardard, Frédéric. „Stabilité des ondes solitaires“. Phd thesis, Cachan, Ecole normale supérieure, 2009. https://theses.hal.science/tel-00426266/fr/.
Der volle Inhalt der QuelleThis thesis is devoted to the stability of solitary waves, and more precisely to the applications of the Maslov index to the spectral stability problem. We show how the stability problem can be related to a family of linear Hamiltonian ODE. It is then possible to define a Maslov index for periodic waves and solitary waves. We compute the limit, when it exists, of the Maslov index of a sequence of periodic waves which converges to a solitary wave. We describe how exterior algebra can be used to compute the Maslov index, both in the periodic and solitary wave cases. We then use this framework for solitary waves and periodic waves arising in the Kawahara equation and for solitary waves arising in a longwave-shortwave interaction system. Lastly, we deal with the stability of stationary solutions of a model for flows over a non-uniform bottom by using a slightly different method
Baccou, Jean. „Analyses multirésolutions et problèmes de bords: applications au traitement d'images et à la résolution numérique d'équations aux dérivées partielles“. Phd thesis, Université de Provence - Aix-Marseille I, 2004. http://tel.archives-ouvertes.fr/tel-00008618.
Der volle Inhalt der QuelleRoussel, Olivier. „Développement d'un algorithme multirésolution adaptatif tridimensionnel pour la résolution des équations aux dérivées partielles paraboliques. Application aux instabilités thermodiffusives de flamme“. Phd thesis, Université de la Méditerranée - Aix-Marseille II, 2003. http://tel.archives-ouvertes.fr/tel-00719904.
Der volle Inhalt der QuelleDione, Ibrahima. „Analyse théorique et numérique des conditions de glissement pour les fluides et les solides par la méthode de pénalisation“. Thesis, Université Laval, 2013. http://www.theses.ulaval.ca/2013/30379/30379.pdf.
Der volle Inhalt der QuelleWe are interested in the classical stationary Stokes and linear elasticity equations posed in a bounded domain [symbol] with a curved and smooth boundary [symbol], associated with slip and ideal contact boundary conditions, respectively. The finite element approximation of such problems can present difficulties because of a Babuška-Sapondžyan’s like paradox: solutions in polygonal domains approaching the smooth domain do not converge to the solution in the limit domain. The objective of this thesis is to explore the application of the penalty method to these slip boundary conditions, in particular in order to overcome this paradox. The penalty method is a classic method widely used in practice because it allows to work in functional spaces without constraints and avoids adding new unknowns like with the Lagrange multiplier method. The first part of this thesis is devoted to the 2D numerical study of different finite elements choices and, most importantly, of different choices of the approximation of the normal vector to the boundary of the domain. With the (discontinuous) normal vector to polygonal domains [symbol] generated with the meshing of [symbol], the finite element solutions do not seem to converge to the exact solution. However, if we use a (continuous) regularization of the normal, isoparametric finite elements of degree 2 for the velocity (or the displacement for elasticity) or a reduced integration of the penalty term, convergence is obtained, with optimal rates in some cases. In a second part, we make a theoretical analysis (in dimensions 2 and 3) of the convergence. The a priori estimates obtained allow to say that even with the (discontinuous) normal vector to polygonal domains, the finite element approximation converges to the exact solution when the penalty parameter is selected appropriately in terms of the size of the elements, showing that the paradox can be circumvented with the penalty method.
Ghorbel, Mohamed-Amin. „Analyse numérique de la dynamique des dislocations et applications à l'homogénéisation“. Phd thesis, Ecole des Ponts ParisTech, 2007. http://pastel.archives-ouvertes.fr/pastel-00002190.
Der volle Inhalt der QuelleChardard, Frédéric. „Stabilité des ondes solitaires“. Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2009. http://tel.archives-ouvertes.fr/tel-00426266.
Der volle Inhalt der QuelleVergnet, Fabien. „Structures actives dans un fluide visqueux : modélisation, analyse mathématique et simulations numériques“. Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS169/document.
Der volle Inhalt der QuelleThe transport of microorganisms and biological fluids by means of cilia and flagella is an universal phenomenon found in almost all living beings. The aim of this thesis is to model, analyze and simulate mathematical fluid-structure interaction problems involving active structures, capable of deforming themselves through internal stresses, and a low Reynolds number fluid, modeled by Stokes equations. In Chapter 2, these active structures are modeled as elastic materials satisfying Saint Venant-Kirchhoff law for elasticity whose activity comes from the addition of an activity term to the second Piola-Kirchhoff stress tensor. Elasticity and Stokes equations are coupled on the fluid-structure interface and the mathematical study of the linearized problem discretized in time is realized. Then, the problem is formulated as a saddle-point problem which isused for numerical simulations. Chapter 3 focuses on the analysis of a quasi-static fluid-structure with an active structure, for which we show existence and uniqueness, for small data, of a strong solution locally in time. Chapter 4 presents a new fictitious domain method (the smooth extension method) for the numerical resolution of transmission problems. The method is first developed for a Laplace transmission problem and further extended to Stokes transmission and fluid-structure interaction problems
El, Rhabi Mohammed. „Analyse Numérique et discrétisation par éléments spectraux avec joints des équations tridimensionnelles de l'électromagnétisme“. Phd thesis, Université Pierre et Marie Curie - Paris VI, 2002. http://tel.archives-ouvertes.fr/tel-00002224.
Der volle Inhalt der QuelleCostes, Joris. „Développement de méthodes de résolution d’équations aux dérivées partielles : du schéma numérique à la simulation d’une installation industrielle“. Thesis, Cachan, Ecole normale supérieure, 2015. http://www.theses.fr/2015DENS0024/document.
Der volle Inhalt der QuelleThe development of efficient simulation tools requires an understanding of physical modeling, mathematical modeling and computer programming. For each of these domains it is necessary to bear in mind the intended application, because the use for a calculation code or simulation software will dictate the level of modeling, and also the programming techniques to be adopted.This dissertation starts with a detailed description applied in the form of fluid flow calculations using the Euler equations. Then simulation of an industrial benchmark is considered using a parallel computational method. Finally, simulation of a complete industrial plant is addressed, where phenomenological relations based on experimental correlations can be used.The first chapter deals with the determination of mesh velocity in the context of ALE (Arbitrary Lagrangian-Eulerian) methods. In the following chapter we focus on the compressible Euler equations solved using the FVCF method (Finite Volume with Characteristic Flux). In this case we consider an interface between a single fluid and a homogeneous two-fluid mixture, where one of the two mixed fluids and the single fluid have the same equation of state.The third chapter is devoted to running high performance simulations using the FluxIC computation code based on the FVCF method with interface capturing. The focus is on sloshing phenomenon encountered during transportation of Liquefied Natural Gas by LNG carriers.The fourth and final chapter deals with modeling of an industrial facility at system level. A systemic approach is presented that provides a level of modeling adapted to the simulation of a large number of components and their interactions. This approach enables users to combine deterministic modeling of physical phenomena with stochastic modeling in order to simulate the behavior of the system for a large set of operating conditions
Ribereau, Dominique. „Génération d'un logiciel de simulation de la combustion d'un bloc de propergol solide“. Bordeaux 1, 1988. http://www.theses.fr/1988BOR10594.
Der volle Inhalt der QuelleGhannam, Fouzia. „Reconstruction de signal par convolution inverse ; application à un problème thermique“. Poitiers, 2000. http://www.theses.fr/2000POIT2280.
Der volle Inhalt der QuelleEl, Amri Hassan. „Analyse numérique et résultats d'existence pour quelques modèles de problèmes physiques : vibrations d'une barre mince sous contraintes, écoulements quasi-newtoniens, écoulements en milieux poreux“. Lyon 1, 1990. http://www.theses.fr/1990LYO10006.
Der volle Inhalt der QuelleKopec, Marie. „Quelques contributions à l'analyse numérique d'équations stochastiques“. Electronic Thesis or Diss., Rennes, École normale supérieure, 2014. http://www.theses.fr/2014ENSR0002.
Der volle Inhalt der QuelleThis 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
Duboscq, Romain. „Analyse et simulation d'équations de Schrödinger déterministes et stochastiques. Applications aux condensats de Bose-Einstein en rotation“. Thesis, Université de Lorraine, 2013. http://www.theses.fr/2013LORR0198/document.
Der volle Inhalt der QuelleThe aim of this Thesis is to study various mathematical and numerical aspects related to the Gross-Pitaevskii and nonlinear Schrödinger equations. We begin (chapter 1) by introducing a few models starting from the physics of Bose-Einstein condensates and optical fibers. This naturally leads to introducing a stochastic Gross-Pitaevskii equation and a nonlinear Schrödinger equation with random dispersion. Next, in the second chapter, we analyze the existence and uniqueness problem for these two equations. We prove that the Cauchy problem admits a solution for the stochastic Gross-Pitaevskii equation with a rotational term by constructing the solution associated with the linear. The third chapter is concerned with the computation of stationary states for the Gross-Pitaevskii equation. We develop a pseudo-spectral approximation scheme for the Continuous Normalized Gradient Flow formulation, combined with preconditioned Krylov subspace methods. This original approach leads to the robust and efficient computation of ground states for fast rotations and strong nonlinearities. In the fourth chapter, we consider some pseudo-spectral schemes for computing the dynamics of the Gross-Pitaevskii and nonlinear Schrödinger equations. These schemes (the Lie's and Strang's splitting schemes and the relaxation scheme) are numerically studied. Moreover, we proceed to a rigorous numerical analysis of the Lie scheme for the associated stochastic PDEs. Finally, we present in the fifth chapter a Matlab toolbox (called GPELab) that provides computational solutions based on the schemes previously introduced in the Thesis
Vilmart, Gilles. „Méthodes numériques géométriques et multi-échelles pour les équations différentielles (in English)“. Habilitation à diriger des recherches, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00840733.
Der volle Inhalt der QuelleGuerrier, Claire. „Multi-scale modeling and asymptotic analysis for neuronal synapses and networks“. Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066518/document.
Der volle Inhalt der QuelleIn the present PhD thesis, we study neuronal structures at different scales, from synapses to neural networks. Our goal is to develop mathematical models and their analysis, in order to determine how the properties of synapses at the molecular level shape their activity and propagate to the network level. This change of scale can be formulated and analyzed using several tools such as partial differential equations, stochastic processes and numerical simulations. In the first part, we compute the mean time for a Brownian particle to arrive at a narrow opening defined as the small cylinder joining two tangent spheres. The method relies on Möbius conformal transformation applied to the Laplace equation. We also estimate, when the particle starts inside a boundary layer near the hole, the splitting probability to reach the hole before leaving the boundary layer, which is also expressed using a mixed boundary-value Laplace equation. Using these results, we develop model equations and their corresponding stochastic simulations to study vesicular release at neuronal synapses, taking into account their specific geometry. We then investigate the role of several parameters such as channel positioning, the number of entering ions, or the organization of the active zone. In the second part, we build a model for the pre-synaptic terminal, formulated in an initial stage as a reaction-diffusion problem in a confined microdomain, where Brownian particles have to bind to small target sites. We coarse-grain this model into two reduced ones. The first model couples a system of mass action equations to a set of Markov equations, which allows to obtain analytical results. We develop in a second phase a stochastic model based on Poissonian rate equations, which is derived from the mean first passage time theory and the previous analysis. This model allows fast stochastic simulations, that give the same results than the corresponding naïve and endless Brownian simulations. In the final part, we present a neural network model of bursting oscillations in the context of the respiratory rhythm. We build a mass action model for the synaptic dynamic of a single neuron and show how the synaptic activity between individual neurons leads to the emergence of oscillations at the network level. We benchmark the model against several experimental studies, and confirm that respiratory rhythm in resting mice is controlled by recurrent excitation arising from the spontaneous activity of the neurons within the network
Doumic, Marie. „Etude asymptotique et simulation numérique de la propagation Laser en milieu inhomogène“. Phd thesis, Université Paris-Diderot - Paris VII, 2005. http://tel.archives-ouvertes.fr/tel-00142670.
Der volle Inhalt der QuelleDans une première partie, nous menons une analyse asymptotique de l'équation de Klein-Gordon. Nous obtenons dans divers cas des problèmes approchés de type Schrödinger ou advection-Schrödinger. Nous montrons que ces problèmes sont bien posés et estimons la différence entre problème exact et problème approché.
Dans une deuxième partie, nous étudions le problème d'advection-Schrödinger sur un domaine borné et non plus sur tout l'espace, et montrons quelle condition au bord il faut imposer pour que la solution de notre problème sur le domaine soit la restriction de la solution sur l'espace entier.
Dans une troisième partie, nous utilisons les résultats précédents pour construire une méthode de résolution numérique, et présentons les simulations obtenues.
Hamed, Mohamed. „Formulations micromorphiques en élastoplasticité non-locale avec endommagement en transformations finies“. Troyes, 2012. http://www.theses.fr/2012TROY0007.
Der volle Inhalt der QuelleIt is well known that the numerical solution of initial and boundary value problems (IBVP) based on constitutive equations exhibiting some induced softening is highly sensitive to the discretization aspects. The main goal of this work is to use the micromorphic continuum theory in order to develop generalized nonlocal constitutive equations for finite elastoplasticity with various micromorphic phenomena. By introducing new micromorphic degrees of freedom (dofs), additional PDEs are obtained from the generalized principle of virtual power. If the space of the state variables is enriched by adding the required micromorphic state variables together with their first gradients, thermodynamically-consistent micromorphic constitutive equations are obtained. Associated numerical aspects are treated in the framework of ABAQUS/Explicit thanks to the users’ subroutines: VUMAT for the implementation of the micromorphic model and the required local numerical integration schemes, and the VUEL to implement new FE with additional dofs. The proposed numerical methodology is validated through a detailed parametric study of the micromorphic model in order to analyze the role of each micromorphic material parameter. Finally, some 2D and 3D examples are performed and their results from local and micromorphic models systematically compared