Tesi sul tema "Méthode de décomposition de domaine optimisée"
Cita una fonte nei formati APA, MLA, Chicago, Harvard e in molti altri stili
Vedi i top-50 saggi (tesi di laurea o di dottorato) per l'attività di ricerca sul tema "Méthode de décomposition de domaine optimisée".
Accanto a ogni fonte nell'elenco di riferimenti c'è un pulsante "Aggiungi alla bibliografia". Premilo e genereremo automaticamente la citazione bibliografica dell'opera scelta nello stile citazionale di cui hai bisogno: APA, MLA, Harvard, Chicago, Vancouver ecc.
Puoi anche scaricare il testo completo della pubblicazione scientifica nel formato .pdf e leggere online l'abstract (il sommario) dell'opera se è presente nei metadati.
Vedi le tesi di molte aree scientifiche e compila una bibliografia corretta.
Japhet, Caroline. "Méthode de décomposition de domaine et conditions aux limites artificielles en mécanique des fluides: méthode Optimisée d'Orde 2". Phd thesis, Université Paris-Nord - Paris XIII, 1998. http://tel.archives-ouvertes.fr/tel-00558701.
Japhet, Caroline. "Méthode de décomposition de domaine et conditions aux limites artificielles en mécanique des fluides : méthode optimisée d'ordre 2 (002)". Paris 13, 1998. http://www.theses.fr/1998PA132044.
Badia, Ismaïl. "Couplage par décomposition de domaine optimisée de formulations intégrales et éléments finis d’ordre élevé pour l’électromagnétisme". Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0058.
In terms of computational methods, solving three-dimensional time-harmonic electromagnetic scattering problems is known to be a challenging task, most particularly in the high frequency regime and for dielectric and inhomogeneous scatterers. Indeed, it requires to discretize a system of partial differential equations set in an unbounded domain. In addition, considering a small wavelength λ in this case, naturally requires very fine meshes, and therefore leads to very large number of degrees of freedom. A standard approach consists in combining integral equations for the exterior domain and a weak formulation for the interior domain (the scatterer) resulting in a formulation coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM). Although natural, this approach has some major drawbacks. First, this standard coupling method yields a very large system having a matrix with sparse and dense blocks, which is therefore generally hard to solve and not directly adapted to compression methods. Moreover, it is not possible to easily combine two pre-existing solvers, one FEM solver for the interior domain and one BEM solver for the exterior domain, to construct a global solver for the original problem. In this thesis, we present a well-conditioned weak coupling formulation between the boundary element method and the high-order finite element method, allowing the construction of such a solver. The approach is based on the use of a non-overlapping domain decomposition method involving optimal transmission operators. The associated transmission conditions are constructed through a localization process based on complex rational Padé approximants of the nonlocal Magnetic-to-Electric operators. The number of iterations required to solve this weak coupling is only slightly dependent on the geometry configuration, the frequency, the contrast between the subdomains and the mesh refinement
Martin, Véronique. "Méthodes de décomposition de domaine de type relaxation d'ondes pour des équations de l'océanographie". Phd thesis, Université Paris-Nord - Paris XIII, 2003. http://tel.archives-ouvertes.fr/tel-00583196.
Berthe, Paul-Marie. "Méthodes de décomposition de domaine de type relaxation d'ondes optimisées pour l'équation de convection-diffusion instationnaire discrétisée par volumes finis". Thesis, Paris 13, 2013. http://www.theses.fr/2013PA132055.
In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Scwharz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multidomain scheme is equivalent to the monodomain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of upwinding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multidomain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results
Hoang, Thi Thao Phuong. "Méthodes de décomposition de domaine espace-temps pour la formulation mixte de problèmes d'écoulement et de transport en milieu poreux". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2013. http://tel.archives-ouvertes.fr/tel-00922325.
Szydlarski, Mikolaj. "Algebraic Domain Decomposition Methods for Darcy flow in heterogeneous media". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2010. http://tel.archives-ouvertes.fr/tel-00550728.
Haferssas, Ryadh Mohamed. "Espaces grossiers pour les méthodes de décomposition de domaine avec conditions d'interface optimisées". Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066450.
The objective of this thesis is to design an efficient domain decomposition method to solve solid and fluid mechanical problems, for this, Optimized Schwarz methods (OSM) are considered and revisited. The optimized Schwarz methods were introduced by P.L. Lions. They consist in improving the classical Schwarz method by replacing the Dirichlet interface conditions by a Robin interface conditions and can be applied to both overlapping and non overlapping subdomains. Robin conditions provide us an another way to optimize these methods for better convergence and more robustness when dealing with mechanical problem with almost incompressibility nature. In this thesis, a new theoretical framework is introduced which consists in providing an Additive Schwarz method type theory for optimized Schwarz methods, e.g. Lions' algorithm. We define an adaptive coarse space for which the convergence rate is guaranteed regardless of the regularity of the coefficients of the problem. Then we give a formulation of a two-level preconditioner for the proposed method. A broad spectrum of applications will be covered, such as incompressible linear elasticity, incompressible Stokes problems and unstationary Navier-Stokes problem. Numerical results on a large-scale parallel experiments with thousands of processes are provided. They clearly show the effectiveness and the robustness of the proposed approach
Caudron, Boris. "Couplages FEM-BEM faibles et optimisés pour des problèmes de diffraction harmoniques en acoustique et en électromagnétisme". Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0062/document.
In this doctoral dissertation, we propose new methods for solving acoustic and electromagnetic three-dimensional harmonic scattering problems for which the scatterer is penetrable and inhomogeneous. The resolution of such problems is key in the computation of sonar and radar cross sections (SCS and RCS). However, this task is known to be difficult because it requires discretizing partial differential equations set in an exterior domain. Being unbounded, this domain cannot be meshed thus hindering a volume finite element resolution. There are two standard approaches to overcome this difficulty. The first one consists in truncating the exterior domain and renders possible a volume finite element resolution. Given that they approximate the scattering problems at the continuous level, truncation methods may however not be accurate enough for SCS and RCS computations. Inhomogeneous penetrable harmonic scattering problems can also be solved by coupling a volume variational formulation associated with the scatterer and surface integral equations related to the exterior domain. This approach is known as FEM-BEM coupling (Finite Element Method-Boundary Element Method). It is of great interest because it is exact at the continuous level. Classical FEM-BEM couplings are qualified as strong because they couple the volume variational formulation and the surface integral equations within one unique formulation. They are however not suited for solving high-frequency problems. To remedy this drawback, other FEM-BEM couplings, said to be weak, have been proposed. These couplings are actually domain decomposition algorithms iterating between the scatterer and the exterior domain. In this thesis, we introduce new acoustic and electromagnetic weak FEM-BEM couplings based on recently developed Padé approximations of Dirichlet-to-Neumann and Magnetic-to-Electric operators. The number of iterations required to solve these couplings is only slightly dependent on the frequency and the mesh refinement. The weak FEM-BEM couplings that we propose are therefore suited to accurate SCS and RCS computations at high frequencies
Caudron, Boris. "Couplages FEM-BEM faibles et optimisés pour des problèmes de diffraction harmoniques en acoustique et en électromagnétisme". Electronic Thesis or Diss., Université de Lorraine, 2018. http://www.theses.fr/2018LORR0062.
In this doctoral dissertation, we propose new methods for solving acoustic and electromagnetic three-dimensional harmonic scattering problems for which the scatterer is penetrable and inhomogeneous. The resolution of such problems is key in the computation of sonar and radar cross sections (SCS and RCS). However, this task is known to be difficult because it requires discretizing partial differential equations set in an exterior domain. Being unbounded, this domain cannot be meshed thus hindering a volume finite element resolution. There are two standard approaches to overcome this difficulty. The first one consists in truncating the exterior domain and renders possible a volume finite element resolution. Given that they approximate the scattering problems at the continuous level, truncation methods may however not be accurate enough for SCS and RCS computations. Inhomogeneous penetrable harmonic scattering problems can also be solved by coupling a volume variational formulation associated with the scatterer and surface integral equations related to the exterior domain. This approach is known as FEM-BEM coupling (Finite Element Method-Boundary Element Method). It is of great interest because it is exact at the continuous level. Classical FEM-BEM couplings are qualified as strong because they couple the volume variational formulation and the surface integral equations within one unique formulation. They are however not suited for solving high-frequency problems. To remedy this drawback, other FEM-BEM couplings, said to be weak, have been proposed. These couplings are actually domain decomposition algorithms iterating between the scatterer and the exterior domain. In this thesis, we introduce new acoustic and electromagnetic weak FEM-BEM couplings based on recently developed Padé approximations of Dirichlet-to-Neumann and Magnetic-to-Electric operators. The number of iterations required to solve these couplings is only slightly dependent on the frequency and the mesh refinement. The weak FEM-BEM couplings that we propose are therefore suited to accurate SCS and RCS computations at high frequencies
Kamel, Slimani. "Estimation a posteriori et méthode de décomposition de domaine". Thesis, Lyon, INSA, 2014. http://www.theses.fr/2014ISAL0025.
This thesis is devoted to numerical analysis in particular a postoriori estimates of the error in the method of asymptotic partial domain decomposition. There are problems in linear elliptic partial and semi-linear with a source which depends only of one variable in a portion of domain. Method of Asymptotic Partial Decomposition of a Domain (MAPDD) originates from the works of Grigori.Panasonko [12, 13]. The idea is to replace an original 3D or 2D problem by a hybrid one 3D − 1D; or 2D − 1D, where the dimension of the problem decreases in part of domain. Effective solution methods for the resulting hybrid problem have recently become available for several systems (linear/nonlinear, fluid/solid, etc.) which allow for each subproblem to be computed with an independent black-box code [21, 17, 18]. The location of the junction between the heterogeneous problems is asymptotically estimated in the works of Panasenko [12]. MAPDD has been designed for handling problems where a small parameter appears, and provides a series expansion of the solution with solutions of simplified problems with respect to this small parameter. In the problem considered in chapter 3 and 4, no small parameter exists, but due to geometrical considerations concerning the domain Ω it is assumed that the solution does not differ very much from a function which depends only on one variable in a part of the domain. The MAPDD theory is not suited for such a context, but if this theory is applied formally it does not provide any error estimate. The a posteriori error estimate proved in this chapter 3 and 4, is able to measure the discrepancy between the exact solution and the hybrid solution which corresponds to the zero-order term in the series expansion with respect to a small parameter when it exists. Numerically, independently of the existence of an asymptotical estimate of the location of the junction, it is essential to detect with accuracy the location of the junction. Let us also mention the interest of locating with accuracy the position of the junction in blood flows simulations [23]. Here in this chapter 3,4 the method proposed is to determine the location of the junction (i.e. the location of the boundary Γ in the example treated) by using optimization techniques. First it is shown that MAPDD can be expressed with a mixed domain decomposition formulation (as in [22]) in two different ways. Then it is proposed to use an a posteriori error estimate for locating the best position of the junction. A posteriori error estimates have been extensively used in optimization problems, the reader is referred to, e.g. [1, 11]
Boubendir, Yassine. "Techniques de décomposition de domaine et méthodes d'équations intégrales". Toulouse, INSA, 2002. http://www.theses.fr/2002ISAT0014.
The aim of this thesis is to develop a non-overlapping domain decomposition method of integral equations for solving scattering harmonic wave problems by perfectly conducting obstacle covered by a dielectric layer. This class of methods was introduced by P. -L. Lions and B. Després and allows us to decrease the size of the discrete problems and improve their condition numbers. We have improved the convergence of the domain decomposition algorithm by introducing the evanescent part of the error. In non-homogeneous dielectric device cases, standard solutions use completely coupled BEM-FEM techniques. The method proposed in this work uncouples the two solutions procedures. One drawback of the domain decomposition method when discretization is performed with nodal finite element, is to define the transmission conditions at the level of the cross points. Theoretical convergence results are only known for discrete mixed finite elements. We have clarified the reason for wich these methods avoid the cross points problem by proving that they are equivalent to a non-conformal scheme. However, these methods are more complex and remain more computationally expensive than nodal finite elements aproaches. We have developed a method that considers the cross points in the case of nodal finite elements. This method allows us to develop a discrete domain decomposition method that is exactly an iterative solution of the initial problem. We have proven the theoretical convergence of this algorithm and have shown on particular cases that the rate of convergence is independent of the mesh
Haeberlein, Florian. "Méthodes de décomposition de domaine espace temps pour le transport réactif --- Application au stockage géologique de CO2". Phd thesis, Université Paris-Nord - Paris XIII, 2011. http://tel.archives-ouvertes.fr/tel-00634507.
Ait-Mansour, Rachid. "Décomposition de domaine et analyse asymptotique appliquée en combustion". Lyon 1, 1997. http://www.theses.fr/1997LYO10197.
Guetat, Rim. "Méthode de parallélisation en temps : application aux méthodes de décomposition de domaine". Paris 6, 2011. http://www.theses.fr/2011PA066629.
Machui, Jürgen. "Simulation magnétostatique de têtes magnétiques en 3D par décomposition du domaine". Paris 11, 1988. http://www.theses.fr/1988PA112055.
This work concerns the simulation of planar magnetic recording heads in the context of its industrial development. Finite elements and reduced potential are used for the 3D calculation of the magnetostatic problem. The particular difficulty of magnetic recording heads lies in the enormous difference in scale between the gap and the whole head. We resolve this difficulty using an iteratif algorithm for domain decomposition for symmetrical heads that converges very rapidly. The non-linear saturation problem can be resolved using the Newton-Raphson method. Our decomposition algorithm is equally efficient for this kind of problem
Chniti, Chokri. "Version unifiée du traitement des singularités en décomposition de domaine". Phd thesis, Ecole Polytechnique X, 2005. http://pastel.archives-ouvertes.fr/pastel-00001439.
Lathuilière, Bruno. "Méthode de décomposition de domaine pour les équations du transport simplifié en neutronique". Phd thesis, Université Sciences et Technologies - Bordeaux I, 2010. http://tel.archives-ouvertes.fr/tel-00468154.
Bencteux, Guy. "Amélioration d'une méthode de décomposition de domaine pour le calcul de structures électroniques". Phd thesis, Ecole des Ponts ParisTech, 2008. http://tel.archives-ouvertes.fr/tel-00391801.
Oumaziz, Paul. "Une méthode de décomposition de domaine mixte non-intrusive pour le calcul parallèle d’assemblages". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLN030/document.
Abstract : Assemblies are critical elements for industrial structures. Strong non-linearities such as frictional contact, as well as poorly controlled preloads make complex all accurate sizing. Present in large numbers on industrial structures (a few million for an A380), this involves managing numerical problems of very large size. The numerous interfaces of frictional contact are sources of difficulties of convergence for the numerical simulations. It is therefore necessary to use robust but also reliable methods. The use of iterative methods based on domain decomposition allows to manage extremely large numerical models. This needs to be coupled with adaptedtechniques in order to take into account the nonlinearities of contact at the interfaces between subdomains. These methods of domain decomposition are still scarcely used in industries. Internal developments in finite element codes are often necessary, and thus restrain this transfer from the academic world to the industrial world.In this thesis, we propose a non-intrusive implementation of these methods of domain decomposition : that is, without development within the source code. In particular, we are interested in the Latin method whose philosophy is particularly adapted to nonlinear problems. It consists in decomposing the structure into sub-domains that are connected through interfaces. With the Latin method the non-linearities are solved separately from the linear differential aspects. Then the resolution is based on an iterative scheme with two search directions that make the global linear problems and the nonlinear local problems dialogue.During this thesis, a totally non-intrusive tool was developed in Code_Aster to solve assembly problems by a mixed domain decomposition technique. The difficulties posed by the mixed aspect of the Latin method are solved by the introduction of a non-local search direction. Robin conditions on the subdomain interfaces are taken into account simply without modifying the sources of Code_Aster. We proposed an algebraic rewriting of the multi-scale approach ensuring the extensibility of the method. We were also interested in coupling the Latin method in domain decomposition to a Krylov algorithm. Applied only to a substructured problem with perfect interfaces, this coupling accelerates the convergence. Preloaded structures with numerous contact interfaces have been processed. Simulations that could not be carried out by a direct computationwith Code_Aster were performed via this non-intrusive domain decomposition strategy
Naceur, Nahed. "Une méthode de décomposition de domaine pour la résolution numérique d’une équation non-linéaire". Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0149.
The subject of this thesis is to present a theoretical analysis and a numerical resolution of a type of quasi-linear elliptic and parabolic equations. These equations present an important role to model phenomena in population dynamics and chemical reactions. We started this thesis with the theoretical study of a quasi-linear elliptical equation for which we demonstrated the existence of a weak non-negative solution under more general hypotheses than those considered in previous works. Then we inspired a new method based on Newton’s method and the domain decomposition method without and with overlapping. Then, we recalled some theoretical aspects concerning the existence, the uniqueness and the regularity of the solution of a parabolic equation called Fujita equation. We also recalled results about the existence of the global solution and the maximum time of existence in the case of blow-up. In order to calculate a numerical approximation of the solution of this type of equation, we introduced a finite element discretization in the space variable and a Crank-Nicholson scheme for the time discretization. To solve the discrete nonlinear problem we implemented a Newton’s method coupled with a domain decomposition method. We have shown that the method is well posed. Another type of parabolic equation known as the Chipot-Weissler equation has also been treated. First, we recalled theoretical results concerning this equation. Then, based on the numerical methods studied previously, a numerical approximation of the solution of this equation was calculated. In the last section of each chapter of this thesis we presented numerical simulations illustrating the performance of the algorithms studied and its compatibility with the theory
Hattori, Takashi. "Décomposition de domaine pour la simulation Full-Wave dans un plasma froid". Electronic Thesis or Diss., Université de Lorraine, 2014. http://www.theses.fr/2014LORR0380.
In order to generate current in tokamak, we look at plasma heating by electromagnetic waves at the lower hybrid (LH) frequency. For this type of description, one use a ray tracing code but we consider a full-wave one, where dielectric properties are local.Our aim is to develop a finite element numerical method for the full-wave modeling and to apply a domain decomposition method. In this thesis, we have developped a finite element method in a cross section of the tokamak for Maxwell equations solving the time harmonic electric field and a nonoverlapping domain decom- position method for the mixed augmented variational formulation by taking continuity accross the interfaces as constraints
Hattori, Takashi. "Décomposition de domaine pour la simulation Full-Wave dans un plasma froid". Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0380/document.
In order to generate current in tokamak, we look at plasma heating by electromagnetic waves at the lower hybrid (LH) frequency. For this type of description, one use a ray tracing code but we consider a full-wave one, where dielectric properties are local.Our aim is to develop a finite element numerical method for the full-wave modeling and to apply a domain decomposition method. In this thesis, we have developped a finite element method in a cross section of the tokamak for Maxwell equations solving the time harmonic electric field and a nonoverlapping domain decom- position method for the mixed augmented variational formulation by taking continuity accross the interfaces as constraints
Mobasher-Amini, Ahmad. "Analyse multi-échelle de structures hétérogènes par décomposition de domaine : application aux navires à passagers". Nantes, 2008. https://tel.archives-ouvertes.fr/tel-00509707.
Numerical simulation of complex industrial structures, containing structural details, leads to very large finite element models. To solve this type of problem, in this work, a domain decomposition method (FETI-DP) is chosen. This study concerns a passenger ship, whose architecture presents a natural sub structuring. The efficiency of these methods depends on its solver; a conjugate gradient solver is used in this work, which has to be equipped with preconditioners. Defining the preconditioner is difficult for heterogeneous structures consisting of three-dimensional assemblies of plates and beams. A method is developed, taking into account the local interface stiffness of the sub-domain to speed up the convergence. In a second part, the goal is to optimize the computational time. To improve the previous approach, a domain decomposition method with different levels of discretization in sub-domains is proposed. The sub-domains in the zones of interest are meshed finely (microscopic) while, the sub-domains in the reminder of the structure are described, by a coarse mesh only (macroscopic or homogenized). Using this strategy raises the problem of the determination of the stiffness of coarse sub-domains, and of incompatible finite element connection between coarse and fine sub-domain. Two different approaches are proposed, such as collocation and mortar. They are validated on simple cases and applied on various heterogeneous examples
Gbikpi, benissan Tete guillaume. "Méthodes asynchrones de décomposition de domaine pour le calcul massivement parallèle". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLC071/document.
An important class of numerical methods features a scalability property well known as the Amdahl’s law, which constitutes the main limiting drawback of parallel computing, as it establishes an upper bound on the number of parallel processing units that can be used to speed a computation up. Extensive research activities are therefore conducted on both mathematical and computer science aspects to increase this bound, in order to be able to squeeze the most out of parallel machines. Domain decomposition methods introduce a natural and optimal approach to solve large numerical problems in a distributed way. They consist in dividing the geometrical domain on which an equation is defined, then iteratively processing each sub-domain separately, while ensuring the continuity of the solution and of its derivative across the junction interface between them. In the present work, we investigate the removal of the scalability bound by the application of the asynchronous iterations theory in various decomposition frameworks, both for space and time domains. We cover various aspects of the development of asynchronous iterative algorithms, from theoretical convergence analysis to effective parallel implementation. Efficient asynchronous domain decomposition methods are thus successfully designed, as well as a new communication library for the quick asynchronous experimentation of existing scientific applications
Samaké, Abdoulaye. "Méthodes non-conformes de décomposition de domaine à grande échelle". Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENM066/document.
This thesis investigates domain decomposition methods, commonly classified as either overlapping Schwarz methods or iterative substructuring methods relying on nonoverlapping subdomains. We mainly focus on the mortar finite element method, a nonconforming approach of substructuring method involving weak continuity constraints on the approximation space. We introduce a finiteelement framework for the design and the analysis of the substructuring preconditioners for an efficient solution of the linear system arising from such a discretization method. Particular consideration is given to the construction of the coarse grid preconditioner, specifically the main variantproposed in this work, using a Discontinuous Galerkin interior penalty method as coarse problem. Other domain decomposition methods, such as Schwarz methods and the so-called three-field method are surveyed with the purpose of establishing a generic teaching and research programming environment for a wide range of these methods. We develop an advanced computational framework dedicated to the parallel implementation of numerical methods and preconditioners introduced in this thesis. The efficiency and the scalability of the preconditioners, and the performance of parallel algorithms are illustrated by numerical experiments performed on large scale parallel architectures
Mansour, Gihane. "Méthode de décomposition de Domaine pour les équations de Laplace et de Helmholtz : Equation de Laplace non linéaire". Paris 13, 2009. http://www.theses.fr/2009PA132013.
This work is divided into two parts : First, a domain decomposition method for the resolution of the Poisson equation and the Helmholtz equation in a bounded domain,with Dirich let boundary condition. Second, The study of the Laplace equation, with non linear boundary condition g. Using the Min-Max method. First, we elaborate some essential tools to introduce our equations, then we present two indirect methods for solving the Poisson equation : there laxed barycentric Dirichlet-Neumann algorithm and the symmetric Dirichlet-Neumann algorithm. The first algorithm was introduced and studied by A. Quarteroni, A. Valli. We present in this work a new proof of its convergence. The second scheme presented is new : we give asymmetric version of the Dirichlet-Neumann condition. We prove that this algorithm is convergent. The theoretical results show that both of the discretization methods are convergent and estimation son the error of convergence are given. We test the two methods numerically, using Comsol with Matlab solver. We notice that the symmetric method converges faster than the barycentric one
Bellalouna, Kamel. "Résolution d'E. D. P. Par méthode spectrale sur un réseau de cylindres". Paris 6, 2007. http://www.theses.fr/2007PA066395.
Ipopa, Mohamed Ali. "Algorithmes de décomposition de domaine pour les problèmes de contact : convergence et simulations numériques". Caen, 2008. http://www.theses.fr/2008CAEN2009.
In this work, we propose two domain decomposition methods to approximate a frictionless contact problem between two elastic bodies. The first one is an improved version of Neumann-Neumann algorithm and the second is a Robin-Robin algorithm. They generalize to variational inequality the Neumann-Neumann and the Lion’s (Robin) nonoverlapping domain decomposition methods. We prove their convergence in continuous and discrete cases. The efficient of those methods are shown by some numerical computations
Abide, Stéphane. "Une méthode de décomposition de domaine pour la simulation numérique directe : contribution à l'étude de jets plans en impact". Nantes, 2005. http://www.theses.fr/2005NANT2081.
Direct Numerical Simulation is a powerful tool in Fluid Mechanics since it allows to describe accurately both in space and time the kinematic and dynamic features of a flow. However, due to the desirable high order discretization, this approach is often restricted to simple geometries. This work proposes a domain decomposition method dedicated to the numerical simulations of turbulent flows which is based on a direct multi-domain solution of the Navier-Stokes equations formulated in primitive variables. The method solves efficiently (parallelization) the incompressible Navier-Stokes equations on " complex " geometries, like inter-connected quadrilaterals, while preserving high order accuracy. Numerous validation test cases are proposed including space/time accuracy, the lid driven cavity, the backward facing step and the flow around a square cylinder. A Direct Numerical Simulation of a square pipe flow is also performed. For fast cooling applications, a preliminary study of the propagation front of the temperature within a thin plate by using plane laminary impinging jet is presented. Finally, an important part of this work is devoted to the study of plane jet impinging on a plane surface and a cubical obstacle for a Reynolds number equal to 3000. A detailed analysis of the statistical, spectral and structural properties of the flow is achieved to obtain a better understanding of the complex phenomena occuring in such a configuration
Parret-Fréaud, Augustin. "Estimation d'erreur de discrétisation dans les calculs par décomposition de domaine". Thesis, Cachan, Ecole normale supérieure, 2011. http://www.theses.fr/2011DENS0022/document.
The control of the quality of mechanical computations arouses a growing interest in both design and certification processes. It relies on error estimators the use of which leads to often prohibitive additional numerical costs on large computations. The present work puts forward a new procedure enabling to obtain a guaranteed estimation of discretization error in the setting of linear elastic problems solved by domain decomposition approaches. The method relies on the extension of the constitutive relation error concept to the framework of non-overlapping domain decomposition through the recovery of admissible interface fields. Its development within the framework of the FETI and BDD approaches allows to obtain a relevant estimation of discretization error well before the convergence of the solver linked to the domain decomposition. An extension of the estimation procedure to heterogeneous problems is also proposed. The behaviour of the method is illustrated and assessed on several numerical examples in 2 dimension
Cresta, Philippe. "Décomposition de domaine et stratégies de relocalisation non-linéaire pour la simulation de grandes structures raidies avec flambage local". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2008. http://tel.archives-ouvertes.fr/tel-00363656.
Spillane, Nicole. "Méthodes de décomposition de domaine robustes pour les problèmes symétriques définis positifs". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2014. http://tel.archives-ouvertes.fr/tel-00958252.
Ciobanu, Oana Alexandra. "Méthode de décomposition de domaine avec adaptation de maillage en espace-temps pour les équations d'Euler et de Navier-Stockes". Thesis, Paris 13, 2014. http://www.theses.fr/2014PA132052/document.
Numerical simulations of more and more complex fluid dynamics phenomena, especially unsteady phenomena, require solving systems of equations with high degrees of freedom. Under their original form, these aerodynamic multi-scale problems are difficult to solve, costly in CPU time and do not allow simulations of large time scales. An implicit formulation, similar to the Schwarz method, with a simple block parallelisation and explicit coupling is no longer sufficient. More robust domain decomposition methods must be conceived so as to make use and adapt to the most of existent hardware.The main aim of this study was to build a parallel in space and in time CFD Finite Volumes code for steady/unsteady problems modelled by Euler and Navier-Stokes equations based on Schwarz method that improves consistency, accelerates convergence and decreases computational cost. First, a study of discretisation and numerical schemes to solve steady and unsteady Euler and Navier–Stokes problems has been conducted. Secondly, an adaptive timespace domain decomposition method has been proposed, as it allows local time stepping in each sub-domain. Thirdly, we have focused our study on the implementation of different parallel computing strategies (OpenMP, MPI, GPU). Numerical results illustrate the efficiency of the method
Lissoni, Giulia. "Méthode DDFV : applications en mécanique des fluides et décomposition des domaines". Thesis, Université Côte d'Azur (ComUE), 2019. http://www.theses.fr/2019AZUR4060.
The goal of this thesis is to study and develop numerical schemes of finite volume type for problems arising in fluid mechanics, namely Stokes and Navier-Stokes problems. The schemes we choosed are of discrete duality type, denoted by DDFV; this method works on staggered grids, where the velocity unknowns are located at the centers of control volumes and at the vertices of the mesh, and the pressure unknowns are on the edges of the mesh. This kind of construction has two main advantages: it allows to consider general meshes (that do not necessarily verify the classical ortogonality condition required by finite volume meshes) and to reconstruct and mimic at the discrete level the dual properties of the continuos differential operators. We start by the study of the discretization of Stokes problem with mixed boundary conditions of Dirichlet/Neumann type; the well-posed character of this problem is strictly relied to Inf-sup inequality, that has to be verified. In the DDFV setting, this inequality has been proven for particular meshes; we can avoid this hypothesis, by adding some stabilization terms in the equation of conservation of mass. In the first place, we study a stabilized scheme for Stokes problem in Laplace form, by showing its well-posedness, some error estimates and numerical tests. We study the same problem in divergence form, where the strain rate tensor replaces the gradient; here, we suppose that the Inf-sup inequality is verified, and we design a well-posed scheme followed by some numerical tests. We consider then the incompressible Navier-Stokes problem. At first, we study this problem coupled with « open » boundary conditions on the outflow; this kind of conditions arises when an artificial boundary is introduced, to save computational ressources or for physical reasons. We write a well-posed scheme and some energy estimates, validated by numerical simulations. Secondly, we address the domain decomposition method without overlap for the incompressible Navier-Stokes problem, by writing a Schwarz algorithm. We discretize the problem with a semi-implicit Euler scheme in time, and at each time iteration we apply Schwarz algorithm to the resulting linear system. We show the convergence of this algorithm and we end by some numerical experiments. This thesis ends with a last chapter concerning the work done during CEMRACS 2019, where the goal is to extend DPIR (a recent technique for interface reconstruction between two materials) to the case of curved interfaces and of three materials. Some numerical simulations show the results
Averous, Fabienne. "Contribution à la prévision du bruit des moteurs d'hélicoptères par éléments finis, équations intégrales, et décomposition de domaine". Compiègne, 2001. http://www.theses.fr/2001COMP1329.
Roux, François-Xavier. "Méthode de décomposition de domaine a l'aide de multiplicateurs de Lagrange et application a la résolution en parallèle des équations de l'élasticité linéaire". Paris 6, 1989. http://www.theses.fr/1989PA066701.
Tournour, Michel. "Modélisation numérique par éléments finis et éléments finis de frontière du comportement vibroacoustique de structures complexes assemblées et couplées à une cavité". Compiègne, 1999. http://www.theses.fr/1999COMP1197.
Kosior, Francis. "Méthode de décomposition par sous-domaines et intégrales de frontières application à l'étude du contact entre deux solides déformables". Vandoeuvre-les-Nancy, INPL, 1997. http://docnum.univ-lorraine.fr/public/INPL_T_1997_KOSIOR_F.pdf.
Després, Bruno. "Méthodes de décomposition de domaine pour la propagation d'ondes en régime harmonique. Le théorème de Borg pour l'équation de Hill vectorielle". Paris 9, 1991. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1991PA090032.
Salque, Bruno. "Décomposition de domaines pour le calcul de la radiosité en simulation d'éclairage". Nancy 1, 1998. http://www.theses.fr/1998NAN10305.
Ait, Younes Tarik. "Calcul de la réponse dynamique de grands domaines à une excitation acoustique par une méthode de sous domaines". Compiègne, 1999. http://www.theses.fr/1999COMP1248.
Safatly, Elias. "Méthode multiéchelle et réduction de modèle pour la propagation d'incertitudes localisées dans les modèles stochastiques". Phd thesis, Université de Nantes, 2012. http://tel.archives-ouvertes.fr/tel-00798526.
Odry, Nans. "Méthode de décomposition de domaine avec parallélisme hybride et accélération non linéaire pour la résolution de l'équation du transport Sn en géométrie non-structurée". Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4058/document.
Deterministic calculation schemes are devised to numerically solve the neutron transport equation in nuclear reactors. Dealing with core-sized problems is very challenging for computers, so much that the dedicated core codes have no choice but to allow simplifying assumptions (assembly- then core-scale steps…). The PhD work aims to correct some of these ‘standard’ approximations, in order to get closer of reference calculations: thanks to important increases in calculation capacities (HPC), nowadays one can solve 3D core-sized problems, using both high mesh refinement and the transport operator. Developments were performed inside the Sn core solver Minaret, from the new CEA neutronics platform Apollo3® for fast neutrons reactors of the CFV-kind.This work focuses on a Domain Decomposition Method in space. The fundamental idea involves splitting a core-sized problem into smaller and 'independent' subproblems. Angular flux is exchanged between adjacent subdomains. In doing so, all combined subproblems converge to the global solution at the outcome of an iterative process. Domain decomposition is well-suited to massive parallelism, allowing much more ambitious computations in terms of both memory requirements and calculation time. An hybrid MPI/OpenMP parallelism is chosen to match the supercomputers architecture. A Coarse Mesh Rebalance accelration technique is added to balance the convergence penalty observed using Domain Decomposition. The potential of the new calculation scheme is demonstrated on a 3D core of the CFV-kind, using an heterogeneous description of the absorbent rods
Rajaona, Tovoarinjara. "Raffinement local de maillage avec une méthode de décomposition de domaine : application au calcul de la dispersion des polluants dans le voisinage d'une source". Rouen, 2000. http://www.theses.fr/2000ROUES038.
Odièvre, David. "Sur une stratégie de calcul en dynamique transitoire en présence de variabilité paramétrique". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2009. http://tel.archives-ouvertes.fr/tel-00442660.
Maurin, Julien. "Résolution des équations intégrales de surface par une méthode de décomposition de domaine et compression hiérarchique ACA : application à la simulation électromagnétique des larges plateformes". Phd thesis, Toulouse, INPT, 2015. http://oatao.univ-toulouse.fr/15113/1/maurin.pdf.
Hinojosa, Rehbein Jorge Andres. "Sur la robustesse d'une méthode de décomposition de domaine mixte avec relocalisation non linéaire pour le traitement des instabilités géométriques dans les grandes structures raidies". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00745225.
Hinojosa, Rehbein Jorge Andrés. "Sur la robustesse d'une méthode de décomposition de domaine mixte avec relocalisation non linéaire pour le traitement des instabilités géométriques dans les grandes structures raidies". Thesis, Cachan, Ecole normale supérieure, 2012. http://www.theses.fr/2012DENS0010/document.
The thesis work focus on the evaluation and the robustness of adapted strategies for the simulation of large structures with not equitably distributed nonlinearities, like local buckling, and global nonlinearities on aeronautical structures. The nonlinear relocalization strategy allows the introduction of nonlinear solving schemes in the sub-structures of the classical domain decomposition methods.At a first step, the performances and the robustness of the method are analysed on academic examples. Then, the strategy is parallelized and studies of speed-up and extensibility are carried out. Finally, the method is tested on larger and more realistic structures
Barrault, Maxime. "Développement de méthodes rapides pour le calcul de structures électroniques". Phd thesis, Ecole des Ponts ParisTech, 2005. http://pastel.archives-ouvertes.fr/pastel-00001655.