Download or read book Estimations D erreur a Posteriori Et Crit res D arr t Pour Des Solveurs Par D composition de Domaine Et Avec Des Pas de Temps Locaux written by Sarah Ali Hassan and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work contributes to the developpement of a posteriori error estimates and stopping criteria for domain decomposition methods with optimized Robin transmission conditions on the interface between subdomains. We study several problems. First, we tackle the steady diffusion equation using the mixed finite element subdomain discretization. Then the heat equation using the mixed finite element method in space and the discontinuous Galerkin scheme of lowest order in time is investigated. For the heat equation, a global-in-time domain decomposition method is used for both conforming and nonconforming time grids allowing for different time steps in different subdomains. This work is then extended to a two-phase flow model using a finite volume scheme in space. For each model, the multidomain formulation can be rewritten as an interface problem which is solved iteratively. Here at each iteration, local subdomain problems are solved, and information is then transferred to the neighboring subdomains. For unsteady problems, the subdomain problems are time-dependent and information is transferred via a space-time interface. The aim of this work is to bound the error between the exact solution and the approximate solution at each iteration of the domain decomposition algorithm. Different error components, such as the domain decomposition error, are identified in order to define efficient stopping criteria for the domain decomposition algorithm. More precisely, for the steady diffusion problem, the error of the domain decomposition method and that of the discretization in space are estimated separately. In addition, the time error for the unsteady problems is identified. Our a posteriori estimates are based on the reconstruction techniques for pressures and fluxes respectively in the spaces H1 and H(div). For the fluxes, local Neumann problems in bands arround the interfaces extracted from the subdomains are solved. Consequently, an effective criterion to stop the domain decomposition iterations is developed. Numerical experiments, both academic and more realistic with industrial data, are shown to illustrate the efficiency of these techniques. In particular, different time steps in different subdomains for the industrial example are used.
Download or read book Etude D estimations D erreur a Posteriori Et D adaptivit Bas e Sur Des Crit res D arr t Et Raffinement de Maillages Pour Des Probl mes D coulements Multiphasiques Et Thermiques written by Soleiman Yousef and published by . This book was released on 2013 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this thesis is the a posteriori error analysis and the conception of adaptive strategies based on stopping criteria and local mesh refinement. We treat a class of multi-dimensional degenerate parabolic equations which represent typical examples of industrial interest. The considered models are discretized by a finite volume scheme in space with the backward Euler temporal stepping. We prove un upper bound for a dual norm of the residual, augmented by a nonconformity evaluation term, by fully computable error estimators. These estimators include: an estimator associated to the linearization error, an estimator associated to the algebraic error, an estimator associated to the temporal error, and an estimator associated to the spatial error. Consequently, these estimators allow to formulate an adaptive resolution algorithm where the corresponding errors can be equilibrated. We also propose a strategy of local mesh reffinement. Finally, we prove the efficiency of our a posteriori estimates. A numerical test illustrates the efficiency of our estimates and the performance of the adaptive algorithm. In particular, a significant gain in terms of the number of mesh cells, the total number of the iterations of the linearization method, and the total number of algebraic solver iterations is achieved on several real-life reservoir engineering examples.
Download or read book ESTIMATION D ERREUR A POSTERIORI POUR L ADAPTATION DE MAILLAGES ELEMENTS FINIS ET DECOMPOSITION DE DOMAINES NON COINCIDENTS EN MECANIQUE DES FLUIDES written by CHUNHUA.. ZHOU and published by . This book was released on 1998 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: DANS CETTE ETUDE, NOUS CONSIDERONS LA METHODE DE DECOMPOSITION DE DOMAINE POUR LE PROBLEME DE STOKES GENERALISE, AVEC L'ADAPTATION DE MAILLAGE DANS CHACUN DES SOUS-DOMAINES EN UTILISANT L'ESTIMATEUR LOCAL D'ERREUR A POSTERIORI COMME INDICATEUR DE L'ADAPTATION. DANS L'ANALYSE NUMERIQUE, LA METHODE DU COMPLEMENT DE SCHUR DUAL A SOUVENT ETE UTILISEE POUR LA DECOMPOSITION DE DOMAINE SANS RECOUVREMENT NI CONFORMITE DE MAILLAGE A L'INTERFACE. ICI, NOUS APPLIQUONS CETTE METHODE A LA RESOLUTION DU PROBLEME DE STOKES GENERALISE PAR LA DECOMPOSITION DE DOMAINE SUR DES GRILLES QUI NE SE RACCORDENT PAS A L'INTERFACE. LA CONDITION DE COMPATIBILITE SUR L'INTERFACE EST IMPOSEE FAIBLEMENT VIA UNE TECHNIQUE DE MULTIPLICATEUR DE LAGRANGE. L'ESTIMATION D'ERREUR A POSTERIORI CORRESPONDANTE AUX APPROXIMATIONS LINEAIRES (POUR LA VITESSE, LA DENSITE OU LA PRESSION, ET LE MULTIPLICATEUR DE LAGRANGE ASSOCIE A LA CONTRAINTE SUR L'INTERFACE) DE CE PROBLEME EST ETABLIE. TOUTES LES ERREURS SONT APPROCHEES DANS L'ESPACE DES FONCTIONS BULLES QUADRATIQUES, UNE BASE HIERARCHIQUE DE L'ESPACE DES FONCTIONS QUADRATIQUES. NOUS FAISONS LA LOCALISATION DE L'ESTIMATION D'ERREUR EN NOUS BASANT SUR LA RESOLUTION DE PROBLEMES LOCAUX. BIEN SUR, NOUS DONNONS LA DEMONSTRATION DE L'EQUIVALENCE ENTRE LES ESTIMATEURS D'ERREUR ET L'ERREUR EXACTE. L'ALGORITHME GENETIQUE, QUI SEMBLE BIEN ADAPTE A LA SITUATION NON-CONVEXE, EST INTRODUIT A L'OPTIMISATION LOCALE DE LA POSITION DE NOEUDS DE MAILLAGE. A LA FIN DE CETTE ETUDE, NOUS FAISONS LES CALCULS PARALLELES EN UTILISANT LA BIBLIOTHEQUE MPI (MESSAGE-PASSING INTERFACE). LA PLUPART DES RESULTATS DE RECHERCHE A VALIDE LA METHODE ET MONTRE L'EFFICACITE DU CALCUL PARALLELE EN UTILISANT CETTE APPROCHE. FINALEMENT NOUS DISCUTONS LES EXTENSIONS POSSIBLES DE NOTRE METHODE DANS LE FUTUR.
Download or read book ESTIMATIONS D ERREUR A POSTERIORI ET TECHNIQUES D ADAPTATION EN ELEMENTS FINIS POUR LA SIMULATION NUMERIQUE D ECOULEMENTS DE FLUIDES VISQUEUX written by JUN.. CAO and published by . This book was released on 1995 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: DANS CETTE ETUDE, NOUS NOUS PROPOSONS DE RESOUDRE PRECISEMENT LES EQUATIONS DE NAVIER-STOKES AVEC DE L'ANALYSE DES ESTIMATIONS D'ERREUR A POSTERIORI ET DES TECHNIQUES D'ADAPTATION DE MAILLAGE EN ELEMENTS FINIS. NOTRE PRESENTATION EST D'ABORD SYSTEMATIQUEMENT CONCENTREE SUR LES DEUX SOUS-PROBLEMES ISSUS D'UNE DECOMPOSITION D'OPERATEUR POUR LA DISCRETISATION EN TEMPS DES EQUATIONS DE NAVIER-STOKES: LE PROBLEME LINEAIRE DE STOKES GENERALISE ET LE PROBLEME NON-LINEAIRE DE CONVECTION-DIFFUSION ; NOUS CONSIDERONS DES DISCRETISATIONS APPROPRIEES EN ESPACE ET DIVERS SOLVEURS RESPECTIVEMENT ASSOCIES A CES DEUX SOUS-PROBLEMES. LA PARTIE CAPITALE DE CE TRAVAIL EST D'ANALYSER THEORIQUEMENT ET NUMERIQUEMENT LES ESTIMATIONS D'ERREUR A POSTERIORI DANS LE CADRE DES EQUATIONS DE STOKES DANS LE CAS LE PLUS GENERAL, AINSI QUE D'APPLIQUER CETTE RECHERCHE A LA RESOLUTION DU PROBLEME DE NAVIER-STOKES, COMME EXPERIENCE DE NATURE NON-LINEAIRE, POUR UN FLUIDE INCOMPRESSIBLE. CONCERNANT LES SCHEMAS D'ADAPTATION DE MAILLAGE, NOUS CHOISISSONS, POUR LES MAILLAGES EMBOITES, SOIT LE RAFFINEMENT, SOIT LE RAFFINEMENT/DERAFFINEMENT SIMULTANE OU, POUR LES MAILLAGES NON-EMBOITES, LE DEPLACEMENT DE POINTS EN GARDANT UNE TOPOLOGIE FIXEE. A PARTIR DES EQUATIONS DE POISSON ET DE CONVECTION-DIFFUSION JUSQU'AU PROBLEME DE NAVIER-STOKES INCOMPRESSIBLE, AUSSI BIEN QUE POUR LE PROBLEME DE STOKES COMPRESSIBLE, DES EXPERIENCES NUMERIQUES DE DIFFERENTS CAS TESTS BIEN SELECTIONNES COUVRENT TOUS CES DOMAINES ET PROUVENT LA VALIDITE DE NOTRE ETUDE
Download or read book Estimations d erreur a posteriori l ments finis mixtes hi rarchiques m thodes de stabilisation et m thodes multiniveaux written by Boujemâa Achchab and published by . This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dans cette thèse, on développe divers estimateurs d'erreur a posteriori, pour l'approximation par éléements finis des équations de type elliptique ou hyperbolique; Ces estimations constituent la base des méthodes adaptatives en éléments finis. Le premier chapitre présente une revue des principaux travaux sur le sujet. On y présente les concepts de base sur des problèmes modèles, les divers types d'estimateurs a posteriori existants, et on précise le champ d'application de chacun de ces types, ses avantages et ses inconvénients. Dans le deuxième chapitre, on s'intéresse aux estimations a priori et a posteriio pour les problèmes de convection et de convection diffutson, on commence par la méthode de GALERKIN classique sur ce genre de problèmes, et on met en lumière l'insuffisance de celle-ci à traiter les cas de petit nombre de Peclet local, ou de la convection pure ; on présente ensuite diverses méthodes de stabilisation (SUPG, GLS, DW), on établit des estimations a priori en fonction des paramètres de stabilisation, des estimations a posteriori ôpur le problème de transport en une norme plus forte que la norme .#0#,#, et ce pour toute méthode de stabilisation en éléments finis C#0, et on finit par proposer des estimations a posteriori pour le problème de convection-diffusion avec SUPG comme méthode de discrétisation. Le troisième chapitre est une généralisation du cadre hiérarchique en estimation d'erreur a posteriori aux cas de l'intégration numérique, ou des éléments finis non conformes. On présente d'abord un cadre abstrait regroupant ces deuxcas, puis le cas des formulaires mixtes comme un cas particulier de ce cadre, et obn expose deux exemples d'application de la stratégie hiérarchique, l'un dans une optique de P-Version en utilisant les espaces de RAVIART-THOMAS, l'autre en H-Version en utilisant l'élément P#1 non conforme - P#0 sur le problèmes de Stokes. Le chapitre 4 est consacré à la constante de l'inégalité de CAUCHY-BUNIAKOVSKI-SCHWARZ forte (C.B.S) qui joue un rôle primordial dans la vitesse de cionvergence des méthodes itératives multiniveaux et l'évaluation de l'indice d'efficacité de certains estimateurs d'erreur a posteriori en éléments finis pour des problèmes elliptiques symétriques. Nous considérons l'approximation du problème de l'élasticité 2D. Concernant la vitesse de convergence des méthodes multiniveaux, le correspondant aux deux maillages triangulaires généraux de dimensions H et 2H, on montre que #2 3/4 uniformément sur le maillage par rapport au coefficient de Poisson. Concernant l'estimateur d'erreur a posteriori, le ...correspondant aux approximations quadratiques et linéaires, sur le même maillage, les calculs numériques ont montré que le ... exact pour l'élément de référence se détériore jusqu'à 1 quand le coefficient de Poisson tend vers 1/2.
Download or read book Estimateurs d erreur a posteriori pour des probl mes dynamiques written by Nadir Soualem and published by . This book was released on 2007 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dans une première partie, on introduit des estimateurs d'erreur a posteriori pour l'équation de la chaleur dans R^d, d=2,3 via une méthode d'éléments finis non conformes en espace et un schéma d'Euler implicite en temps. Pour cette discrétisation, on élabore un indicateur d'erreur résiduel spatial basé sur les sauts des dérivées normales et tangentielles de notre approximation, ainsi qu'un indicateur résiduel temporel basé sur le saut du gradient à chaque pas de temps. Les bornes inférieures et supérieures de la norme de l'erreur forment les résultats principaux de cette étude. En outre, on montre que ces estimateurs sont fiables et efficaces. Dans une seconde partie, on traite le problème de Stokes dynamique. L'élaboration des estimateurs a posteriori est également basée sur des estimateurs spatiaux et temporels. Une preuve de leur fiabilité et de leur efficacité est donnée. Finalement, les tests numériques et un algorithme adaptatif confirment les prévisions théoriques et le bon comportement de ces estimateurs.
Download or read book Sur l erreur a posteriori de methodes duales d elements finis written by Abdel-Ilah Ghabbar and published by . This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce travail concerne l'analyse de l'erreur à posteriori de l'approximation par des formulations duales d'équations elliptiques du second ordre. Dans un premier temps, on donne des estimations à posteriori par sous-domaines de l'erreur due à l'usage de méthodes équilibre en dimension finie. L'obtention de ces estimations nécessitent la résolution de problèmes locaux. Ils ont été, d'une part, résolus par une méthode des bases hiérarchiques et d'autre part, estimés par la méthode des résidus. Une comparaison des résultats est donnée. Dans un deuxième temps, le problème modèle est résolu par une méthode hybride en dimension finie. On propose un estimateur basé sur les résidus locaux. Des essais numériques complètent l'étude théorique, pour une géométrie simple. Enfin, dans le cas de la méthode mixte, l'étude menée a permis de construire un estimateur d'erreur base sur une méthode de post-traitement. On montre qu'il est asymptotiquement exact. Ensuite, on donne un estimateur similaire pour une formulation primale équivalente à la formulation mixte.
Download or read book Cardiovascular Mathematics written by Luca Formaggia and published by Springer Science & Business Media. This book was released on 2010-06-27 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes. This book offers a mathematically sound and up-to-date foundation to the training of researchers and serves as a useful reference for the development of mathematical models and numerical simulation codes.
Download or read book Medical Image Computing and Computer Assisted Intervention MICCAI 2012 written by Nicholas Ayache and published by Springer. This book was released on 2012-08-28 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume set LNCS 7510, 7511, and 7512 constitutes the refereed proceedings of the 15th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2012, held in Nice, France, in October 2012. Based on rigorous peer reviews, the program committee carefully selected 252 revised papers from 781 submissions for presentation in three volumes. The third volume includes 79 papers organized in topical sections on diffusion imaging: from acquisition to tractography; image acquisition, segmentation and recognition; image registration; neuroimage analysis; analysis of microscopic and optical images; image segmentation; diffusion weighted imaging; computer-aided diagnosis and planning; and microscopic image analysis.
Download or read book Subsurface water Flow and Solute Transport written by and published by . This book was released on 1989 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Predicting Structured Data written by Neural Information Processing Systems Foundation and published by MIT Press. This book was released on 2007 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art algorithms and theory in a novel domain of machine learning, prediction when the output has structure.
Download or read book Analyse de la Signature Radar Et de la Vid oscopie de Cibles Militaires written by North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development. Sensor and Propagation Panel. Symposium and published by . This book was released on 1997 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Practical Time Series Analysis written by Aileen Nielsen and published by O'Reilly Media. This book was released on 2019-09-20 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time series data analysis is increasingly important due to the massive production of such data through the internet of things, the digitalization of healthcare, and the rise of smart cities. As continuous monitoring and data collection become more common, the need for competent time series analysis with both statistical and machine learning techniques will increase. Covering innovations in time series data analysis and use cases from the real world, this practical guide will help you solve the most common data engineering and analysis challengesin time series, using both traditional statistical and modern machine learning techniques. Author Aileen Nielsen offers an accessible, well-rounded introduction to time series in both R and Python that will have data scientists, software engineers, and researchers up and running quickly. You’ll get the guidance you need to confidently: Find and wrangle time series data Undertake exploratory time series data analysis Store temporal data Simulate time series data Generate and select features for a time series Measure error Forecast and classify time series with machine or deep learning Evaluate accuracy and performance
Download or read book Current International Treaties written by Thomas Bruce Millar and published by Taylor & Francis. This book was released on 1984-01 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Computational Learning Theory written by Michael J. Kearns and published by MIT Press. This book was released on 1994-08-15 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Computational learning theory is a new and rapidly expanding area of research that examines formal models of induction with the goals of discovering the common methods underlying efficient learning algorithms and identifying the computational impediments to learning. Each topic in the book has been chosen to elucidate a general principle, which is explored in a precise formal setting. Intuition has been emphasized in the presentation to make the material accessible to the nontheoretician while still providing precise arguments for the specialist. This balance is the result of new proofs of established theorems, and new presentations of the standard proofs. The topics covered include the motivation, definitions, and fundamental results, both positive and negative, for the widely studied L. G. Valiant model of Probably Approximately Correct Learning; Occam's Razor, which formalizes a relationship between learning and data compression; the Vapnik-Chervonenkis dimension; the equivalence of weak and strong learning; efficient learning in the presence of noise by the method of statistical queries; relationships between learning and cryptography, and the resulting computational limitations on efficient learning; reducibility between learning problems; and algorithms for learning finite automata from active experimentation.
Download or read book Working with the Anthropological Theory of the Didactic in Mathematics Education written by Marianna Bosch and published by Routledge. This book was released on 2019-10-23 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the main research veins developed within the framework of the Anthropological Theory of the Didactic (ATD), a paradigm that originated in French didactics of mathematics. While a great number of publications on ATD are available in French and Spanish, Working with the Anthropological Theory of the Didactic in Mathematics Education is the first directed at English-speaking international audiences. Written and edited by leading researchers in ATD, the book covers all aspects of ATD theory and practice, including teaching applications. The chapters feature the most relevant and recent investigations presented at the 6th international conference on the ATD, offering a unique opportunity for an international audience interested in the study of mathematics teaching and learning to keep in touch with advances in educational research. The book is divided into four sections and the contributions explore key topics such as: The core concept of ‘praxeology’, including its development and functionalities The need for new teaching praxeologies in the paradigm of questioning the world The impact of ATD on the teaching profession and the education of teachers This is the second volume in the New Perspectives on Research in Mathematics Education. This comprehensive casebook is an indispensable resource for researchers, teachers and graduate students around the world.
Download or read book Applied Reactor Physics written by Alain Hébert and published by Presses inter Polytechnique. This book was released on 2009 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
