Letteratura scientifica selezionata sul tema "Méthode parareal"
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Articoli di riviste sul tema "Méthode parareal":
GUETAT, Rim. "Coupling Parareal with Non-Overlapping Domain Decomposition Method". Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées Volume 23 - 2016 - Special... (13 dicembre 2016). http://dx.doi.org/10.46298/arima.1474.
Tesi sul tema "Méthode parareal":
Poirier, Yohan. "Contribution à l'accélération d'un code de calcul des interactions vagues/structures basé sur la théorie potentielle instationnaire des écoulements à surface libre". Electronic Thesis or Diss., Ecole centrale de Nantes, 2023. http://www.theses.fr/2023ECDN0042.
Numerous numerical methods have been developed to model and study the interactions between waves and structures. The most commonly used are those based on potential free-surface flow theory. In the Weak-Scatterer approach, the free-surface boundary conditions are linearized with respect to the position of the incident wave, so the disturbances on the wave must be of low amplitude compared to the incident wave, but no assumptions are made about the motion of the bodies and the amplitude of the incident wave, thus increasing the scope of application. When this approach is coupled with a boundary element method, it is necessary to construct and solve a dense linear system at each time iteration. The high spatial complexity of these steps limits the use of this method to relatively small systems. This thesis aims to reduce this constraint by implementing methods for accelerating calculations. It is shown that the use of the multipole method reduces the spatial complexity in time and memory space associated with solving the linear system, making it possible to study larger systems. Several preconditioning methods have been studied in order to reduce the number of iterations required to find the solution to the system using an iterative solver. In contrast to the fast multiparallelization method, the Parareal time parallelization method can, in principle, accelerate the entire simulation. We show that it speeds up calculation times in the case of fixed floats free in the swell, but that the acceleration factor decreases rapidly with the camber of the swell
Sall, Guillaume. "Quelques algorithmes rapides pour la finance quantitative". Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066474/document.
In this thesis, we will focus on the critical node of the computation of counterparty credit risk, the fast evaluation of financial derivatives and their sensitivities. We propose several mathematical and computer-based methods to address this issue. We have contributed to four areas: an extension of the Vibrato method and an application of the weighted multilevel Monte Carlo for the computation of the greeks for high order derivatives n>1 with automatic differentiation. The third contribution concerns the evaluation of American style option, here we use a parareal scheme to speed up the assessing process and we made an application for solving backward stochastic differential equations. The last contribution is the conception of an efficient computation engine for financial derivatives with a parallel architecture
Gilliocq-Hirtz, Diane. "Techniques variationnelles et calcul parallèle en imagerie : Estimation du flot optique avec luminosité variable en petits et larges déplacements". Thesis, Mulhouse, 2016. http://www.theses.fr/2016MULH8379/document.
The work presented in this thesis focuses on the estimation of the optical flow through variational methods in small and large displacements. We propose a model based on the combined local-global strategy to which we add the consideration of brightness intensity variations. The particularity of this manuscript is the use of the finite element method to solve the equations. Indeed, for now, this method is really rare in the field of the optical flow. Thanks to this choice of resolution, we implement an adaptive control of the regularization and a mesh adaptation to refine the solution on the edges of the image. To reduce computation times, we parallelize the programs. The first method implemented is a parallel in time method called parareal. By combining a coarse and a fine solver, this algorithm speeds up the computations. To save even more time and to also be able to handle high resolution sequences, we then use a domain decomposition method. Combined with the massively parallel solver MUMPS, this method allows a significant reduction of computation times. Finally, we propose to couple the domain decomposition method and the parareal to have the benefits of both methods. In the second part, we apply all these models to the case of the optical flow estimation in large displacements. We use the parareal method to cope with the non-linearity of the problem. We end by a concrete example of application of the optical flow in film restoration
Reyes, Riffo Sebastián. "Méthodes mathématiques pour l'extraction d'énergie marine". Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLED068.
The present thesis aims to contribute to the development of a theoretical framework for three problems in the context of renewable marine energy. In the first part, we propose a procedure to couple unbounded in time data assimilation methods with time-parallel algorithms. The combination between the Luenberger observer and Parareal algorithm is studied, providing a way to estimate the number of parareal iterations required to preserve the observer rate of convergence, as well as an estimation of the theoretical efficiency of the entire procedure.We then discuss the determination of a bathymetry from an optimization perspective. Imposing that wave propagation must fulfill a certain criterion associated with a cost functional, we consider a PDE-constrained optimization problem where the bathymetry plays the role of control and wave propagation is described by the Helmholtz equation. We are able to prove, under suitable assumptions, the continuity of the control-to-state mapping and the existence of an optimal solution, including also some results about solutions to Helmholtz problem and convergence in a discrete framework.This work is complemented by numerical experiments.The last part of this work is devoted to analyze the convergence of the Blade element momentum (BEM) theory, a classical method used to determine the propeller efficiency as well as its design parameters. We propose a reformulation of the method that allows to obtain conditions for existence of solutions and establish the convergence of some solving algorithms. We also study the associated optimization problem in certain contexts
Guibert, David. "Analyse de méthodes de résolution parallèles d'EDO/EDA raides". Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00430013.
Guibert, David. "Analyse de méthodes de résolution parallèles d’EDO/EDA raides". Thesis, Lyon 1, 2009. http://www.theses.fr/2009LYO10138/document.
This PhD Thesis deals with the development of parallel numerical methods for solving Ordinary and Algebraic Differential Equations. ODE and DAE are commonly arising when modeling complex dynamical phenomena. We first show that the parallelization across the method is limited by the number of stages of the RK method or DIMSIM. We introduce the Schur complement into the linearised linear system of time integrators. An automatic framework is given to build a mask defining the relationships between the variables. Then the Schur complement is coupled with Jacobian Free Newton-Krylov methods. As time decomposition, global time steps resolutions can be solved by parallel nonlinear solvers (such as fixed point, Newton and Steffensen acceleration). Two steps time decomposition (Parareal, Pita,...) are developed with a new definition of their grids to solved stiff problems. Global error estimates, especially the Richardson extrapolation, are used to compute a good approximation for the second grid. Finally we propose a parallel deferred correction
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
Duarte, Max. "Méthodes numériques adaptatives pour la simulation de la dynamique de fronts de réaction multi-échelles en temps et en espace". Phd thesis, Ecole Centrale Paris, 2011. http://tel.archives-ouvertes.fr/tel-00667857.
Bedez, Mathieu. "Modélisation multi-échelles et calculs parallèles appliqués à la simulation de l'activité neuronale". Thesis, Mulhouse, 2015. http://www.theses.fr/2015MULH9738/document.
Computational Neuroscience helped develop mathematical and computational tools for the creation, then simulation models representing the behavior of certain components of our brain at the cellular level. These are helpful in understanding the physical and biochemical interactions between different neurons, instead of a faithful reproduction of various cognitive functions such as in the work on artificial intelligence. The construction of models describing the brain as a whole, using a homogenization microscopic data is newer, because it is necessary to take into account the geometric complexity of the various structures comprising the brain. There is therefore a long process of rebuilding to be done to achieve the simulations. From a mathematical point of view, the various models are described using ordinary differential equations, and partial differential equations. The major problem of these simulations is that the resolution time can become very important when important details on the solutions are required on time scales but also spatial. The purpose of this study is to investigate the various models describing the electrical activity of the brain, using innovative techniques of parallelization of computations, thereby saving time while obtaining highly accurate results. Four major themes will address this issue: description of the models, explaining parallelization tools, applications on both macroscopic models
Ait, Ameur Katia. "Contributions à la simulation parallèle d’écoulements diphasiques et analyse de schémas volumes finis sur grille décalée". Thesis, Sorbonne université, 2020. http://www.theses.fr/2020SORUS077.
In this thesis, the most important contribution has consisted in the implementation of modern algorithms that are well adapted for modern parallel architectures, in an industrial software dedicated to nuclear safety studies, the Cathare code. This software is dedicated to the simulation of two-phase flows within nuclear reactors under nominal or accidental situations. This work represents in itself an important contribution in nuclear safety studies thanks to the reduction of the computational time and the better accuracy that it can provide for the knowledge of the state of nuclear power plants during severe accidents. A special effort has been made in order to efficiently parallelise the time variable through the use of the parareal algorithm. For this, we have first designed a parareal scheme that takes more efficiently into account the presence of multi-step time schemes. This family of time schemes can potentially bring higher approximation orders than plain one-step methods but the initialisation of the time propagation in each time window needs to be appropriately chosen. The main idea consists in defining a consistent approximation of the solutions involved in the initialisation of the time propagations, allowing to reach convergence with the desired accuracy. Then, this method has been succesfully applied on test cases that are representative of the numerical challenges for the simulation of two-phase flows in the context of nuclear safety studies. A second phase of our work has been to explore numerical methods that could handle better the numerical difficulties that are specific to two-phase flows with a lower computational cost. This part of the thesis has been devoted to the understanding of the theoretical properties of finite volume schemes on staggered grids such as the one used in the Cathare code. Staggered schemes are known to be more precise for almost incompressible flows in practice and are very popular in the thermal hydraulics community. However, in the context of compressible flows, their stability analysis has historically been performed with a heuristic approach and the tuning of numerical parameters. This question has been addressed by analysing their numerical diffusion operator that gives new insight into these schemes. For classical staggered schemes, the stability is obtained only in the case of constant sign velocities. We propose a class of linearly L 2 -stable staggered schemes and a class of entropic staggered schemes. These new classes are based on a carefully chosen numerical diffusion operator and are more adapted to two-phase flows where phasic velocities frequently change signs. These methods have been successfully applied in analytical cases (involving Euler equations) and we expect that the present developments will allow its use in more realistic and complex cases in the future, like the one of the simulation of two-phase flows within a nuclear reactor during an accidental scenario