Tesi sul tema "Problèmes de valeurs propres mixtes"
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Michetti, Marco. "Steklov and Neumann eigenvalues : inequalities, asymptotic and mixed problems". Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0109.
This thesis is devoted to the study of Neumann eigenvalues, Steklov eigenvalues and relations between them. The initial motivation of this thesis was to prove that, in the plane, the product between the perimeter and the first Steklov eigenvalue is always less then the product between the area and the first Neumann eigenvalue. Motivated by finding counterexamples to this inequality, in the first part of this thesis, we give a complete description of the asymptotic behavior of the Steklov eigenvalues in a dumbbell domain consisting of two Lipschitz sets connected by a thin tube with vanishing width. Using these results in the two dimensional case we find that the inequality is not always true. We study the inequality in the convex setting, proving a weaker form of the inequality for all convex domains and proving the inequality for a special class of convex polygons. We then also give the asymptotic behavior for Neumann and Steklov eigenvalues on collapsing convex domains, linking in this way these two eigenvalues with Sturm-Liouville type eigenvalues. In the second part of this thesis, using the results concerning the asymptotic behavior of Neumann eigenvalues on collapsing domains and a fine analysis of Sturm-Liouville eigenfunctions we study the maximization problem of Neumann eigenvalues under diameter constraint. In the last part of the thesis we study the mixed Steklov-Dirichlet. After a first discussion about the regularity properties of the Steklov-Dirichlet eigenfunctions we obtain a stability result for the eigenvalues. We study the optimization problem under a measure constraint on the set in which we impose Steklov boundary conditions, we prove the existence of a minimizer and the non-existence of a maximizer. In the plane we prove a continuity result for the eigenvalues under some topological constraint
Mitjana, Florian. "Optimisation topologique de structures sous contraintes de flambage". Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30343/document.
Topology optimization aims to design a structure by seeking the optimal material layout within a given design space, thus making it possible to propose innovative optimal designs. This thesis focuses on topology optimization for structural problems taking into account buckling constraints. In a wide variety of engineering fields, innovative structural design is crucial. The lightening of structures during the design phase holds a prominent place in order to reduce manufacturing costs. Thus the goal is often the minimization of the mass of the structure to be designed. Regarding the constraints, in addition to the conventional mechanical constraints (compression, tension), it is necessary to take into account buckling phenomena which are characterized by an amplification of the deformations of the structure and a potential annihilation of the capabilities of the structure to support the applied efforts. In order to adress a wide range of topology optimization problems, we consider the two types of representation of a structure: lattice structures and continuous structures. In the framework of lattice structures, the objective is to minimize the mass by optimizing the number of elements of the structure and the dimensions of the cross sections associated to these elements. We consider structures constituted by a set of frame elements and we introduce a formulation of the problem as a mixed-integer nonlinear problem. In order to obtain a manufacturable structure, we propose a cost function combining the mass and the sum of the second moments of inertia of each frame. We developed an algorithm adapted to the considered optimization problem. The numerical results show that the proposed approach leads to significant mass gains over existing approaches. In the case of continuous structures, topology optimization aims to discretize the design domain and to determine the elements of this discretized domain that must be composed of material, thus defining a discrete optimization problem. [...]
Aboud, Fatima. "Problèmes aux valeurs propres non-linéaires". Phd thesis, Université de Nantes, 2009. http://tel.archives-ouvertes.fr/tel-00410455.
L(z)=H_0+z H_1+...+ zm-1Hm-1+zm , où H0,H1,...,Hm-1 sont des opérateurs définis sur l'espace de Hilbert H et z est un paramètre complexe. On s'intéresse au spectre de la famille L(z). Le problème L(z)u(x)=0 est un problème aux valeurs propres non-linéaires lorsque m≥2 (Un nombre complexe z est appelé valeur propre de L(z), s'il existe u dans H, u≠0$ tel que L(z)u=0). Ici nous considérons des familles quadratiques (m=2) et nous nous intéressons en particulier au cas LP(z)=-∆x+(P(x)-z)2, définie dans l'espace de Hilbert L2(Rn), où P est un polynôme positif elliptique de degré M≥2. Dans cet exemple les résultats connus d'existence de valeurs propres concernent les cas $n=1$ et $n$ paire.
L'objectif principal de ce travail est de progresser vers la preuve de la conjecture suivante, formulée par Helffer-Robert-Wang : « Pour toute dimension n, pour tout M≥2, le spectre de LP est non vide. »
Nous prouvons cette conjecture dans les cas suivants : (1) n=1,3, pour tout polynôme P de degré M≥2. (2) n=5, pour tout polynôme P convexe vérifiant de plus des conditions techniques. (3) n=7, pour tout polynôme P convexe.
Ce résultat s'étend à des polynômes quasi-homogènes et quasi-elliptiques comme par exemple P(x,y)=x2+y4, x dans Rn1, y dans Rn2, n1+n2=n, et n paire.
Nous prouvons ces résultats en calculant les coefficients d'une formule de trace semi-classique et en utilisant le théorème de Lidskii.
Aboud, Fatima Mohamad. "Problèmes aux valeurs propres non-linéaires". Nantes, 2009. http://www.theses.fr/2009NANT2067.
In this work we study the polynomial family of operators L(¸) = H0+¸H1+· · ·+¸m−1Hm−1+¸m, where the coefficients H0,H1, · · · ,Hm−1 are operators dened on the Hilbert space H and ¸ is a complex parameter. We are interested to study the spectrum of the family L(¸). The problem L(¸)u(x) = 0, is called a non-linear eigenvalue problem for m ¸ 2 (The number ¸0 2 C is called an eigenvalue of L(¸), if there exists u0 2 H, u0 6= 0 such that L(¸0)u0 = 0). We consider here a quadratic family (m = 2) and in particular we are interested in the case LP (¸) = −¢x + (P(x) − ¸)2, which is dened on the Hilbert space L2(Rn), where P is an elliptic positive polynomial of degree M ¸ 2. For this example results for existence of eigenvalues are known for n = 1 and n is even. The main goal of our work is to check the following conjecture, stated by Heler-Robert-Wang : For every dimension n, for every M ¸ 2, the spectrum of LP is non empty. We prouve this conjecture for the following cases : • n = 1, 3, for every polynomial P of degree M ¸ 2. • n = 5, for every convex polynomial P satisfying some technical conditions. • n = 7, for every convex polynomial P. This result extends to the case of quasi-homogeneous polynomial and quasi-elliptic, for example P(x, y) = x2 + y4, x 2 Rn1 , y 2 Rn2 , n1 + n2 = n, and n is even. We prove this results by computing the coefficients of a semi-classical trace formula and by using the theorem of Lidskii
Chrayteh, Houssam. "Problèmes de valeurs propres pour des opérateurs multivoques". Poitiers, 2012. http://theses.univ-poitiers.fr/25162/2012-Chrayteh-Houssam-These.pdf.
The aim of our research is to study the existence and regularity of solutions for eigenvalue problems involving a →p-multivoque operator A : V → P(V*) on a smooth domain Ω C Rᶰ. Through N-functions, we construct a →p-multivoque Leray-Lions "strongly monotonic" operator on an anisotropic Orlicz-Sobolev space. We note that the theoretical formulation of problems related to such operator is essentially based on the notion of Clarke subdifferential. For this reason, we introduce new variational methods that match the resolution of these issues in the "subcritical" case where compactness plays an important role and critical case when we lose compactness. Various applications are given to illustrate our abstract results, for example, an anisotropic operator with variable exponents and an operator with a Hardy type weight
Conrad, Francis. "Perturbation de problèmes aux valeurs propres non linéaires et problèmes à frontière libre". Phd thesis, Université Claude Bernard - Lyon I, 1986. http://tel.archives-ouvertes.fr/tel-00830638.
Emad, Petiton Nahid. "Contribution à la résolution de grands problèmes de valeurs propres". Paris 6, 1989. http://www.theses.fr/1989PA066174.
Rammal, Hadia. "Problèmes de Complémentarité aux Valeurs Propres : Théories, Algorithmes et Applications". Limoges, 2013. http://aurore.unilim.fr/theses/nxfile/default/08806eb2-33e6-4642-b821-b7218aaac0f2/blobholder:0/2013LIMO4036.pdf.
This manuscript deals with the development of mathematical methods applicable to the theoretical and numerical study of a wide class of unilateral problems. To put it more precisely, we consider the Pareto and Lorentz cones eigenvalue complementarity problems PCVP. Such problems appear in many scientific disciplines such as physics, mechanics and engineering. Firstly, we are interested to the resolution of PCVP using an adequate method, “Lattice Projection Method LPM”, leading to an efficient and effective result. The originality of this formulation in comparison with the existing literature is that it is not based on the complementarity approach. Then, our contribution is reflected in the study of the non-singularity conditions of the Jacobian matrices used in the semismooth Newton method SNM to detect solutions of such problems. Then, by using the performance profiles, we compare LPM with other solvers known in the literature. The results prove in accordance with the experimental observations and show the efficiency of LPM. Secondly, we treat the stochastic case of PCVP in the sense of Pareto and Lorentz cones. We reformulate such problem to find the zeros of a semismooth function. Furthermore, we study the non-singularity conditions of the Jacobian matrix of this function to solve such problems. Moreover, we transform the problem as a constrained minimization reformulation. Finally, we discuss the inverse Pareto eigenvalue complementarity problem PICVP. This task focuses more precisely on the resolution of PICVP where we present a new method, “Inverse Lattice Projection Method ILPM”, to solve such problems
Djellit, Ali. "Valeurs propres de problèmes elliptiques indéfinis sur des ouverts non bornés". Toulouse 3, 1992. http://www.theses.fr/1992TOU30072.
Kiwan, Rola. "Problèmes d'optimisation liés aux valeurs propres du Laplacien et aux pavages du plan [et] problèmes d'évolutions semi-linéaires". Tours, 2007. http://www.theses.fr/2007TOUR4001.
In this thesis, we consider first the optimal placement problem for the first Dirichlet Laplacian eingenvalue for plane domains with dihidral symetry, we then consider the same problem for the second eigenvalue of spherical shells. We solve the isoperimetric problem for plane domains who tile the plane by the action of a given lattice. Finally we study sufficient conditions for explosion in finite time for the solution of a non local parabolic problem as well as hyperbolic inequality
Fender, Alexandre. "Solutions parallèles pour les grands problèmes de valeurs propres issus de l'analyse de graphe". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLV069/document.
Graphs, or networks, are mathematical structures to represent relations between elements. These systems can be analyzed to extract information upon the comprehensive structure or the nature of individual components. The analysis of networks often results in problems of high complexity. At large scale, the exact solution is prohibitively expensive to compute. Fortunately, this is an area where iterative approximation methods can be employed to find accurate estimations. Historical methods suitable for a small number of variables could not scale to large and sparse matrices arising in graph applications. Therefore, the design of scalable and efficient solvers remains an essential problem. Simultaneously, the emergence of parallel architecture such as GPU revealed remarkable ameliorations regarding performances and power efficiency. In this dissertation, we focus on solving large eigenvalue problems a rising in network analytics with the goal of efficiently utilizing parallel architectures. We revisit the spectral graph analysis theory and propose novel parallel algorithms and implementations. Experimental results indicate improvements on real and large applications in the context of ranking and clustering problems
Makhoul, Ola. "Inégalités universelles pour les valeurs propres d'opérateurs naturels". Thesis, Tours, 2010. http://www.theses.fr/2010TOUR4006/document.
In this thesis, we generalize the Yang and the Levitin and Parnovski universalinequalities, concerning the eigenvalues of the Dirichlet Laplacian on a Euclideanbounded domain, to the case of the Hodge-de Rham Laplacian on a Euclidean closed submanifold.This gives an extension of Reilly’s inequality and Asada’s inequality, concerningthe first eigenvalues of the Laplacian and the Hodge-de Rham Laplacian respectively, toall eigenvalues of these operators. We also obtain a new abstract inequality relating theeigenvalues of a self-adjoint operator on a Hilbert space to two families of symmetric andskew-symmetric operators and their commutators. This inequality is proved useful both forunifying and for improving numerous known results concerning the Laplacian, the Hodgede Rham Laplacian, the square of the Dirac operator and more generally the Laplacianacting on sections of a Riemannian vector bundle on a Euclidean submanifold, the KohnLaplacian, a power of the Laplacian...In the last part, we obtain an upper bound for thefirst eigenvalue of Steklov problem on a domain Ω of a Euclidean or a spherical submanifoldin terms of the r-th mean curvatures of ∂Ω
Sango, Mamadou. "Valeurs propres et vecteurs propres de problèmes elliptiques non-autoadjoints avec un poids indéfini pour des systèmes d'équations aux dérivées partielles". Valenciennes, 1998. https://ged.uphf.fr/nuxeo/site/esupversions/73e24869-db40-4b04-99c0-2d4c9520e3a0.
Vasseur, Baptiste. "Étude de problèmes différentiels elliptiques et paraboliques sur un graphe". Thesis, Littoral, 2014. http://www.theses.fr/2014DUNK0400/document.
After a quick presentation of usual notations for the graph theory, we study the set of harmonic functions on graphs, that is, the functions whose laplacian is zero. These functions form a vectorial space. On a uniformly locally finite tree, we shaw that this space has dimension one or infinity. When the graph has an infinite number of cycles, this result change and we describe some examples showing that there exists a graph on which the harmonic functions form a vectorial space of dimension n, for all n. We also treat the case of a particular periodic graph. Then, we study more precisely the eigenvalues of infinite dimension. In this case, the eigenspace contains a subspace isomorphic to the set of bounded sequences. An inequality concerning the spectral is given when edges length is equal to one. Examples show that these inclusions are optimal. We also study the asymptotic behavior of eigenvalues for elliptic operators under dynamical Kirchhoff node conditions. We write the problem as a Sturm-Liouville operator and we transform it in a matrix problem. Then we find a characteristic equation whose zeroes correspond to eigenvalues. We deduce a formula for the asymptotic behavior. In the last chapter, we study the stability of stationary solutions for some reaction-diffusion problem whose the non-linear term is polynomial
Triki, Faouzi. "Etude des résonances et des fréquences de scattering dans l'électromagnétisme". Palaiseau, École polytechnique, 2002. http://www.theses.fr/2002EPXX0038.
Cossonnière, Anne. "Valeurs propres de transmission et leur utilisation dans l'identification d'inclusions à partir de mesures électromagnétiques". Thesis, Toulouse, INSA, 2011. http://www.theses.fr/2011ISAT0011/document.
The theory of inverse scattering for acoustic or electromagnetic waves is an active area of research with significant developments in the past few years. The Linear Sampling Method (LSM) is a method that allows the reconstruction of the shape of an object from its acoustic or electromagnetic response with a few a priori knowledge on the physical properties of the scatterer. However, this method fails for resonance frequencies called transmission eigenvalues in the case of penetrable objects. These transmission eigenvalues are the eigenvalues of a new type of problem called the interior transmission problem. Their main feature is that not only they can give information on the physical properties of the scatterer but they can also be computed from far field measurements. In this thesis, we prove the existence and the discreteness of the set of transmission eigenvalues for two new configurations corresponding to the cases of a scatterer containing a cavity or a perfect conductor. A new approach using surface integral equations is also developed to compute numerically transmission eigenvalues for general geometries
Le, Peutrec Dorian. "Études de petites valeurs propres du Laplacien de Witten". Phd thesis, Université Rennes 1, 2009. http://tel.archives-ouvertes.fr/tel-00452849.
Petrides, Romain. "Bornes sur des valeurs propres et métriques extrémales". Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10234/document.
This thesis is devoted to the study of the Laplace eigenvalues and the Steklov eigenvalues on Riemannian manifolds. We look for optimal bounds among the set of metrics, lying in a conformal class or not. We also characterize, if they exist the metrics which reach these bounds. These extremal metrics have properties from the theory of minimal surfaces. First, we are interested in the upper bound of Laplace eigenvalues in a class of conformal metrics, called the conformal eigenvalues. In Chapter 1, we estimate the second conformal eigenvalue of the standard sphere. In Chapters 2 and 3, we prove that the first conformal eigenvalue of a Riemannian manifold is greater than the one of the standard sphere of same dimension, with equality only for the standard sphere. Then, we look for existence and regularity results for metrics which maximize eigenvalues on surfaces, in a given conformal class or not. In Chapters 3 and 4, we prove an existence result for Laplace eigenvalues. In Chapter 6, the work is done for Steklov eigenvalues. Finally, in Chapter 5, obtained in collaboration with Paul Laurain, we prove a regularity and quantification result for harmonic maps with free boundary on a Riemannian surface. It is a key component for Chapter 6
Sini, Mourad. "Résultats spectraux sur le système de l'élasticité et identification de coefficients discontinus pour le problème de Borg-Levinson". Aix-Marseille 1, 2002. http://www.theses.fr/2002AIX11049.
Mezher, Dany. "Calcul parallèle de pseudo-spectres". Rennes 1, 2001. http://www.theses.fr/2001REN10054.
Achtaïch, Naceur. "Injections du type Sobolev et applications à la résolution de problèmes de valeurs propres non linéaires axisymétriques". Lyon 1, 1985. http://www.theses.fr/1985LYO10179.
Dusson, Geneviève. "Estimation d'erreur pour des problèmes aux valeurs propres linéaires et non-linéaires issus du calcul de structure électronique". Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066238/document.
The objective of this thesis is to provide error bounds for linear and nonlinear eigenvalue problems arising from electronic structure calculation. We focus on ground-state calculations based on Density Functional Theory, including Kohn-Sham models. Our bounds mostly rely on a posteriori error analysis. More precisely, we start by studying a phenomenon of discretization error cancellation for a simple linear eigenvalue problem, for which analytical solutions are available. The mathematical study is based on an a priori analysis for the energy error. Then, we present an a posteriori analysis for the Laplace eigenvalue problem discretized with finite elements. For simple eigenvalues of the Laplace operator and their corresponding eigenvectors , we provide guaranteed, fully computable and efficient error bounds. Thereafter, we focus on nonlinear eigenvalue problems. First, we provide an a posteriori analysis for the Gross-Pitaevskii equation. The error bounds are valid under assumptions that can be numerically checked, and can be separated in two components coming respectively from the discretization and the iterative algorithm used to solve the nonlinear eigenvalue problem. Balancing these error components allows to optimize the computational resources. Second, we present a post-processing method for the Kohn-Sham problem, which improves the accuracy of planewave computations of ground state orbitals at a low computational cost. The post-processed solutions can be used either as a more precise solution of the problem, or used for computing an estimation of the discretization error. This estimation is not guaranteed, but in practice close to the real error
Cristofol, Michel. "Etude mathématique de la propagation d'ondes guidées dans un milieu élastique tridimensionnel non borné stratifié et localement perturbé". Aix-Marseille 1, 1998. http://www.theses.fr/1998AIX11009.
Ratiney, Hélène. "Quantification automatique de signaux de spectrométrie et d'imagerie spectroscopique de résonance magnétique fondée sur une base de métabolites : une approche semi-paramétrique". Lyon 1, 2004. http://www.theses.fr/2004LYO10195.
Gajardo, Pedro. "Théorie spectrale des opérateurs multivoques et applications aux systèmes dynamiques : caractérisation de certaines propriétés des fonctions non-lisses". Avignon, 2004. http://www.theses.fr/2004AVIG0403.
This thesis falls within the general context of the theory of set-valued systems. The first part of the thesis is devoted to the spectral theory of set-valued operators and its applications to the analysis of discrete and continuous differential inclusions. We study the concepts of eigenvalue and eigenvector for set-valued operators defined on a Banach space. In particular, we discuss some continuity results for these concepts. Next we extend Landau's concept of epsilon-eigenvalue for linear operators to the general context of positively homogeneous set-valued mappings defined on Hilbert spaces. We explore in detail; this new concept and, as way of application, we discuss the resonance phenomenon of a firstorder differential inclusion. Another area of application of the spectral theory of set-valued operators is the asymptotic stability analysis of a discrete dynamical system described by a convex process. We study the asymptotic behavior of such systems by using first- and higher-order spectral information. In the context of a first-order differential inclusion given by a convex process, we propose a new method for constructing smooth solutions and we study the dependence with respect to initial data. The last part of this thesis is devoted to the subdifferential calculus. As it is well known, several properties of extended-real-valued lower semicontinuous functions are equivalent to suitable conditions of the corresponding Clarke subdifferential. In this thesis we show that any such condition on the Clarke subdifferential still holds with any set-valued operator admitting the Clarke subdifferential representation formula
Hassannezhad, Asma. "Bornes supérieures pour les valeurs propres d'opérateurs naturels sur les variétés riemanniennes compactes". Thesis, Tours, 2012. http://www.theses.fr/2012TOUR4036/document.
The purpose of this thesis is to find upper bounds for the eigenvalues of natural operators acting on functions on a compact Riemannian manifold (M; g) such as the Laplace–Beltrami operator and Laplace-type operators. In the case of the Laplace-Beltrami operator, two aspects are investigated: The first aspect is to study relationships between the intrinsic geometry and eigenvalues of the Laplacian operator. In this regard, we obtain upper bounds depending only on the dimension and a conformal invariant called min-conformal volume. Asymptotically, these bounds are consistent with the Weyl law. They improve previous results by Korevaar and Yang and Yau. The method which is introduced to obtain the results, is powerful and interesting in itself. The second aspect is to study the interplay of the extrinsic geometry and eigenvalues of the Laplace–Beltrami operator acting on compact submanifolds of RN and of CPN. We investigate an extrinsic invariant called the intersection index studied by Colbois, Dryden and El Soufi. For compact submanifolds of RN, we extend their results and obtain upper bounds which are stable under small perturbation. For compact submanifolds of CPN, we obtain an upper bound depending only on the degree of submanifolds. For Laplace type operators, a modification of our method lead to have upper bounds for the eigenvalues of Schrödinger operators in terms of the min-conformal volume and integral quantity of the potential. As another application of our method, we obtain upper bounds for the eigenvalues of the Bakry–Émery Laplace operator depending on conformal invariants
Attoh, Komdedzi Kwami. "Contributions à l'analyse numérique du problème généralisé de valeurs propres et applications". Saint-Etienne, 1993. http://www.theses.fr/1993STET4006.
François, Gilles. "Comportement spectral asymptotique provenant de problèmes paraboliques sous conditions au bord dynamiques". Littoral, 2002. http://www.theses.fr/2002DUNK0083.
In this thesis, one studies the asymptotic behaviour of the eigenvalues associated with parabolic problems under dynamical boundary conditions. In the whole text, one puts our results on relation with the classical ones (e. G. Those related to the Dirichlet or Neumann boudary conditions). After obtaining a first result for the order of magnitude of the sequence (in the case of laplacian in an arbitrary domain), one considers two particular cases (the unit disc and the unit square in R2) and makes more explicit calculus for both domains. Then one extends the results of the first chapter to an elliptic operator with divergential form, and improves the order of magnitude of the sequence ina domaine of R2. Lastly, one makes a spectral analysis of a diffusion problem in a particular ramified space
Michel, Philippe. "Principe d'entropie relative généralisée et dynamique de populations structurées". Paris 9, 2005. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=2005PA090032.
This thesis deals with the dynamic of population balance equations (PBE) as the Cell Division Equation (CDE) or as the classical McKendrick age model. More precisely, we show a family of relative entropies (General Relative Entropy-GRE) in a large class of PBE. The existence of such a family and a sharp study of the asymptotic behavior is related to the existence and uniqueness of the solution to an eigenproblem. For instance, the study of this eigenproblem in a CDE model, allows us to show the link between the Malthusian growth rate of a cell population an the symmetry of its division. We prove, in a simple nonlinear age model, the global convergence to a steady state and we compare the results given by the GRE method and the linearization method
Bogosel, Beniamin. "Optimisation de formes et problèmes spectraux". Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAM066/document.
We study some shape optimization problems associated to spectral and geometric functionals from both theoretical and numerical points of view. One of the main ideas is to provide Gamma-convergence frameworks allowing the construction of numerical approximation methods for the quantities we wish to optimize. In particular, these numerical methods are applied to the study of the Dirichlet-Laplace eigenvalues under perimeter constraint in two and three dimensions and to optimization problems concerning multiphase configurations and partitions in the plane and on three dimensional surfaces.As well, we focus on the analysis of the Steklov spectrum in different geometric classes of domains. Together with the study of existence of extremal domains and the spectral stability under geometric perturbations, we develop methods based on fundamental solutions in order to compute numerically the spectrum. A detailed analysis of the numerical method shows that we get an important precision, while the computation time is significantly decreased compared to mesh-based methods. This approach is extended to the computation of Wentzell and Laplace-Beltrami eigenvalues
MALIGE, FRANCOIS. "Etude mathematique et numerique de l'homogeneisation des assemblages combustibles d'un cur de reacteur nucleaire". Palaiseau, Ecole polytechnique, 1996. http://www.theses.fr/1996EPXX0041.
Harrabi, Ali. "Pseudospectres d'opérateurs intégraux et différentiels : application à la physique mathématique". Toulouse 1, 1998. http://www.theses.fr/1998TOU10031.
Ahusborde, Etienne. "Méthode d'ordre élevé pour l'opérateur -grad(div(. )) et applications". Bordeaux 1, 2007. http://www.theses.fr/2007BOR13425.
Harmouch, Jouhayna. "Décomposition de petit rang, problèmes de complétion et applications : décomposition de matrices de Hankel et des tenseurs de rang faible". Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4236/document.
We study the decomposition of a multivariate Hankel matrix as a sum of Hankel matrices of small rank in correlation with the decomposition of its symbol σ as a sum of polynomialexponential series. We present a new algorithm to compute the low rank decomposition of the Hankel operator and the decomposition of its symbol exploiting the properties of the associated Artinian Gorenstein quotient algebra . A basis of is computed from the Singular Value Decomposition of a sub-matrix of the Hankel matrix . The frequencies and the weights are deduced from the generalized eigenvectors of pencils of shifted sub-matrices of Explicit formula for the weights in terms of the eigenvectors avoid us to solve a Vandermonde system. This new method is a multivariate generalization of the so-called Pencil method for solving Pronytype decomposition problems. We analyse its numerical behaviour in the presence of noisy input moments, and describe a rescaling technique which improves the numerical quality of the reconstruction for frequencies of high amplitudes. We also present a new Newton iteration, which converges locally to the closest multivariate Hankel matrix of low rank and show its impact for correcting errors on input moments. We study the decomposition of a multi-symmetric tensor T as a sum of powers of product of linear forms in correlation with the decomposition of its dual as a weighted sum of evaluations. We use the properties of the associated Artinian Gorenstein Algebra to compute the decomposition of its dual which is defined via a formal power series τ. We use the low rank decomposition of the Hankel operator associated to the symbol τ into a sum of indecomposable operators of low rank. A basis of is chosen such that the multiplication by some variables is possible. We compute the sub-coordinates of the evaluation points and their weights using the eigen-structure of multiplication matrices. The new algorithm that we propose works for small rank. We give a theoretical generalized approach of the method in n dimensional space. We show a numerical example of the decomposition of a multi-linear tensor of rank 3 in 3 dimensional space. We show a numerical example of the decomposition of a multi-symmetric tensor of rank 3 in 3 dimensional space. We study the completion problem of the low rank Hankel matrix as a minimization problem. We use the relaxation of it as a minimization problem of the nuclear norm of Hankel matrix. We adapt the SVT algorithm to the case of Hankel matrix and we compute the linear operator which describes the constraints of the problem and its adjoint. We try to show the utility of the decomposition algorithm in some applications such that the LDA model and the ODF model
Shahzadeh, Fazeli Seyed Abolfazi. "Stratégies de redémarrage des méthodes itératives d'algèbre linéaire pour le calcul global". Versailles-St Quentin en Yvelines, 2005. http://www.theses.fr/2005VERS0011.
L'objectif de ce travail est de contribuer à la résolution des grands problèmes de valeur propre et/ou des grands systèmes linéaires en utilisant des ressources partagées sur des réseaux plus ou moins larges. La résolution de grands systèmes d'algèbre linéaire s'effectue, à l'aide des méthodes itératives hybrides. Une méthode hybride combine plusieurs méthodes numériques différentes ou bien plusieurs copy d'une même méthode numérique paramétrées différemment afin d'accélérer la convergence de l'une de ces méthodes. L'amélioration de la vitesse de convergence et d'exécution des méthodes hybrides par des méthodologies numériques et/ou des techniques de calcul parallèle et distribué constitue l'objectif principal de cette thèse. La vitesse de convergence de ces méthodes est dépendante de l'approche utilisée lors du redémarrage du processus itératif. Nous présentons une étude sur une méthode hybride appelée Multiple Explicitly Restarted Arnoldi Method (MERAM), et nous proposons deux approches synchrones pour sa mise en oeuvre. Nous proposons également un nouvel algorithme hybride synchrone pour la méthode Implicitly Restarted Arnoldi Method. Des environnements de calcul global basés sur une approche Grid-RPC constituent un bon choix pour élaborer des programmes de résolution de problèmes sur les grilles de calcul. Un exemple typique de tels environnements est le système NetSolve. L'utilisation de ce type d'architectures nécessite la définition de nouveaux algorithmes. Une adaptation de MERAM asynchrone au système de calcul global NetSolve a été conçue. Nous avons montré que les algorithmes asynchrones de type MERAM sont très bien adaptés au calcul global. Nous avons mis en évidence un certain nombre de problèmes ouverts concernant la programmation des algorithmes hybrides en calcul global
Liberge, Erwan. "Modèles réduits obtenus par la méthode de POD-Galerkin pour les problèmes d'interaction fluide structure". Phd thesis, Université de La Rochelle, 2008. http://tel.archives-ouvertes.fr/tel-00348432.
Nous avons donc dans un premier temps présenté et rappelé les principaux résultats de la POD. Ces résultats ont été illustrés sur l'équation de Burgers monodimensionnelle et un écoulement à faible Reynolds autour d'un cylindre. La décomposition Bi-orthogonale (BOD) a également été testée pour ces deux cas, celle-ci n'améliorant pas les résultats obtenus par la POD. La POD pour l'étude de structures en vibration a également été testée.
Ensuite, nous avons étudié son application pour des problèmes d'interaction fluide structure. La complexité tient dans le caractère mobile des domaines alors que la base POD est spatiale et indépendante du temps. Pour remédier à cet inconvénient, on propose d'établir une base POD pour un champ de vitesse global défini sur un domaine fixe. On introduit pour cela un domaine de référence fixe contenant l'ensemble des configurations mobiles sur un intervalle de temps. On obtient ainsi une base POD pour un champ de vitesse fluide et solide. On a ensuite proposé l'écriture d'un modèle réduit pour des problèmes traitant d'interaction entre un fluide et un solide rigide. Pour cela, une formulation multiphasique du type domaine fictifs a été utilisée. Cette méthode est testée avec succès sur un cas monodimensionnel et trois cas bidimensionnels, traitant un fluide initialement au repos, ensuite un écoulement à nombre de Reynolds modéré, et un dernier exemple à fort nombre de Reynold.
Bui, Dung. "Modèles d'ordre réduit pour les problèmes aux dérivées partielles paramétrés : approche couplée POD-ISAT et chainage temporel par algorithme pararéel". Thesis, Châtenay-Malabry, Ecole centrale de Paris, 2014. http://www.theses.fr/2014ECAP0021/document.
In this thesis, an efficient Reduced Order Modeling (ROM) technique with control of accuracy for parameterized Finite Element solutions is proposed. The ROM methodology is usually necessary to drastically reduce the computational time and allow for tasks like parameter analysis, system performance assessment (aircraft, complex process, etc.). In this thesis, a ROM using Proper Orthogonal Decomposition (POD) will be used to build local models. The “model” will be considered as a database of simulation results store and retrieve the database is studied by extending the algorithm In Situ Adaptive Tabulation (ISAT) originally proposed by Pope (1997). Depending on the use and the accuracy requirements, the database is enriched in situ (i.e. online) by call of the fine (reference) model and construction of a local model with an accuracy region in the parameter space. Once the trust regions cover the whole parameter domain, the computational cost of a solution becomes inexpensive. The coupled POD-ISAT, here proposed, provides a promising effective ROM approach for parametric finite element model. POD is used for the low-order representation of the spatial fields and ISAT for the local representation of the solution in the design parameter space. This method is tested on a Engineering case of stationary air flow in an aircraft cabin. This is a coupled fluid-thermal problem depending on several design parameters (inflow temperature, inflow velocity, fuselage thermal conductivity, etc.). For evolution problems, we explore the use of time-parallel strategies, namely the parareal algorithm originally proposed by Lions, Maday and Turinici (2001). A quasi-Newton variant of the algorithm called Broyden-parareal algorithm is here proposed. It is applied to the computation of the gas diffusion in an aircraft cabin. This thesis is part of the project CSDL (Complex System Design Lab) funded by FUI (Fond Unique Interministériel) aimed at providing a software platform for multidisciplinary design of complex systems
Guérin, Pierre. "Méthodes de décomposition de domaine pour la formulation mixte duale du problème critique de la diffusion des neutrons". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2007. http://tel.archives-ouvertes.fr/tel-00210588.
Privat, Yannick. "Quelques problèmes d'optimisation de formes en sciences du vivant". Phd thesis, Université Henri Poincaré - Nancy I, 2008. http://tel.archives-ouvertes.fr/tel-00331243.
Dans la première partie de cette thèse, nous considérons l'exemple d'une fibre nerveuse de type axone ou dendrite. Nous proposons deux critères pour expliquer sa forme. Le premier traduit l'atténuation dans le temps du message électrique traversant la fibre et le second l'atténuation dans l'espace de ce message. Dans notre choix de modélisation, nous distinguons deux types de fibres nerveuses : celles qui sont connectées au noyau de la cellule et celles qui sont connectées entre elles. Les problèmes correspondants se ramènent à la minimisation par rapport au domaine des valeurs propres d'un opérateur elliptique et d'une fonction de transfert faisant intervenir la trace sur le bord du domaine du potentiel électrique au sein de la fibre.
La seconde partie de cette thèse est dédiée à l'optimisation de la forme d'un arbre bronchique ou d'une partie de cet arbre. Nous considérons un critère de type "énergie dissipée". Dans une étude théorique, nous prouvons tout d'abord que le cylindre n'est pas une conduite optimale pour minimiser l'énergie dissipée par un fluide newtonien incompressible satisfaisant aux équations de Navier-Stokes.
Nous effectuons ensuite des simulations en deux et trois dimensions afin de tester numériquement si l'arbre bronchique est ou non optimal.
Chehab, Jean-Paul. "Méthode des inconnues incrémentales : application au calcul des bifurcations". Paris 11, 1993. http://www.theses.fr/1993PA112031.
Beaudouin, Marie. "Analyse modale pour les coques minces en révolution". Phd thesis, Université Rennes 1, 2010. http://tel.archives-ouvertes.fr/tel-00541467.
Amattat, Mohamed. "Problèmes aux valeurs propres et bifurcations globales pour l'opérateur p-laplacien.[suivi de] Bifurcations dans les systèmes de réaction-diffusion: attracteurs du modèle simplifié du "Bruxellateur"". Doctoral thesis, Universite Libre de Bruxelles, 1988. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/213324.
Balloumi, Imen. "Expansion asymptotique pour des problèmes de Stokes perturbés - Calcul des intégrales singulières en Électromagnétisme". Thesis, Cergy-Pontoise, 2018. http://www.theses.fr/2018CERG0958/document.
This thesis contains three main parts. The first part concerns the derivation of an asymptotic expansion for the solution of Stokes resolvent problem with a small perturbation of the domain. Firstly, we verify the continuity of the solution with respect to the small perturbation via the stability of the density function. Secondly, we derive the asymptotic expansion ofthe solution, after deriving the expansion of the density function. The procedure is based on potential theory for Stokes problem in connection with boundary integral equation method, and geometric properties of the perturbed boundary. The main objective of the second part on this report, is to present a schematic way to derive high-order asymptotic expansions for both eigenvalues and eigenfunctions for the Stokes operator caused by small perturbationsof the boundary. Also, we rigorously derive an asymptotic formula which is in some sense dual to the leading-order term in the asymptotic expansion of the perturbations in the Stokes eigenvalues due to interface changes of the inclusion. The implementation of the boundary element method requires the evaluation of integrals with a singular integrand. A reliable andaccurate calculation of these integrals can in some cases be crucial and difficult. In the third part of this report we propose a method of evaluation of singular integrals based on recursive reductions of the dimension of the integration domain. It leads to a representation of the integralas a linear combination of one-dimensional integrals whose integrand is regular and that can be evaluated numerically and even explicitly. The Maxwell equation is used as a model equation, but these results can be used for the Laplace and the Helmholtz equations in 3-D.For the discretization of the domain we use planar triangles, so we evaluate integrals over the product of two triangles. The technique we have developped requires to distinguish between several geometric configurations
Chakir, Rachida. "Contribution à l'analyse numérique de quelques problèmes en chimie quantique et mécanique". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2009. http://tel.archives-ouvertes.fr/tel-00459149.
Duong, Ahn Tuan. "Théories spectrale et de résonances pour l'opérateur de Schrödinger avec champ magnétique". Paris 13, 2013. http://scbd-sto.univ-paris13.fr/secure/edgalilee_th_2013_duong.pdf.
Karaa, Samir. "Problèmes d'extrémums relatifs à des valeurs propres et applications : recherche de la forme optimale d'une colonne en compression : [thèse en partie soutenue sur un ensemble de travaux]". Toulouse 3, 1996. http://www.theses.fr/1996TOU30188.
Benis, Arriel. "Aide à l'exploration et à la découverte de relations dans des données de la Génomique Médicale Fonctionnelle". Paris 13, 2009. http://www.theses.fr/2009PA132032.
Data Mining is an emerging area in Medical Informatics research field. Nowadays, clinical research protocols are no longer limited to collect only medical data, but they are also regarding to other kinds of data such as genomic data from cDNA microarrays. Currently, the approaches commonly used by biologists in this context simply explore a tiny part of the data based on a priori. Our work is based on automating the analysis process. Firstly, this PhD dissertation focuses on the definition of a data workflow adapted to data that we deal with (bioclinical and genomics data). Secondly, outliers, due to the relative quality of data and sources of errors in analysis are automatically identified thanks to a classification method. Finally, all these results will be presented in an easy way to biologist experts. Experiments related to researches in obesity medicine have been done and allowed to validate our Data Mining process and to discover biomarkers. Evaluations of use and usability have shown the benefits of our approach
Drouart, Fabien. "Étude de la non-linéarité Kerr dans les fibres optiques microstructurées". Aix-Marseille 3, 2008. http://www.theses.fr/2008AIX30047.
We want to find spatial solitons in optical fibres with a nonlinear optical Kerr effect. That's why we propose a new numerical approach using the Finite Element Method. A nonlinear scalar model is used to validate our method and to understand the physical meaning of the new solutions in a simple case. Several examples dealing with step-index fibres and microstructured optical fibres with a finite size cross section are described. In each geometry, a complete study is achieved to prove with numeric tests the existence of a single self-coherent nonlinear solution (spatial soliton) with the highest reachable energy avoiding the self-focusing instability. The spatial soliton depends on the finite transverse profile of the structure, is the Townes soliton in the nonlinear homogeneous medium but it is different from the Townes in optical fibres: it's the generalization of the Townes soliton. The full-vector case is also implemented to obtain for the first time a vector Townes soliton
Privat, Yannick. "Quelques problèmes d’optimisation de formes en sciences du vivant". Thesis, Nancy 1, 2008. http://www.theses.fr/2008NAN10045/document.
In this Ph.D thesis, we wonder whether some shapes observed in Nature could follow from the optimization of a criterion. More precisely, we consider an organ or a part of the human body and we try to guess a criterion that Nature could have tried to optimize. Then, we solve the resulting shape optimization problem in order to compare the shape obtained by a theoretical or a numerical way with the real shape of the organ. If these two shapes are similar, it may be deduced that the criterion is relevant. In the first part of this thesis, we consider the example of a nerve fiber of an axon or a dendrite kind. We propose two criterions to explain its shape. The first one stands for the attenuation throughout the time of the electrical message and the second one stands for the attenuation throughout the space of that message. In our choice of modeling, we distinguish two sorts of nerve fibers: these connected to the nucleus of the cell and these connected with two other fibers. The corresponding problems boil down to the minimization with respect to the domain of the eigenvalues of an elliptic operator and of a transfer function expressed with the trace of the electrical potential in the fiber on the boundary of the domain. The second part of this thesis is devoted to optimization of the shape of a bronchial tree or a part of that tree. We consider as a criterion the ``dissipated energy''. In a theoretical study, we foremost prove that the cylinder is not an optimal pipe to minimize energy dissipated by a newtonian incompressible fluid driven by a Navier Stokes system. Afterwards, we propose two and three dimensional simulations to verify numericaly if the bronchial tree is or not optimal
Lambert-Nebout, Catherine. "Étude des moyens d'analyse du signal basse fréquence d'un récepteur d'alignement de piste". Toulouse, INPT, 1989. http://www.theses.fr/1989INPT086H.