La simulation numérique de systèmes d’équations différentielles raides ordinaires ou algébriques est devenue partie intégrante dans le processus de conception des systèmes mécaniques à dynamiques complexes. L’objet de ce travail est de développer des méthodes numériques pour réduire les temps de calcul par le parallélisme en suivant deux axes : interne à l’intégrateur numérique, et au niveau de la décomposition de l’intervalle de temps. Nous montrons l’efficacité limitée au nombre d’étapes de la parallélisation à travers les méthodes de Runge-Kutta et DIMSIM. Nous développons alors une méthodologie pour appliquer le complément de Schur sur le système linéarisé intervenant dans les intégrateurs par l’introduction d’un masque de dépendance construit automatiquement lors de la mise en équations du modèle. Finalement, nous étendons le complément de Schur aux méthodes de type "Krylov Matrix Free". La décomposition en temps est d’abord vue par la résolution globale des pas de temps dont nous traitons la parallélisation du solveur non-linéaire (point fixe, Newton-Krylov et accélération de Steffensen). Nous introduisons les méthodes de tirs à deux niveaux, comme Parareal et Pita dont nous redéfinissons les finesses de grilles pour résoudre les problèmes raides pour lesquels leur efficacité parallèle est limitée. Les estimateurs de l’erreur globale, nous permettent de construire une extension parallèle de l’extrapolation de Richardson pour remplacer le premier niveau de calcul. Et nous proposons une parallélisation de la méthode de correction du résidu. / 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

Made available in DSpace on 2014-10-09T12:51:51Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:06:32Z (GMT). No. of bitstreams: 0 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP / FAPESP:00/11446-0

Made available in DSpace on 2014-10-09T12:51:51Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:06:32Z (GMT). No. of bitstreams: 0 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Foram estudados os processos de transferência de energia (TE) dos níveis 4I13/2 ; 4I11/2 do Er3+ e 5I7 ; 5I6 do Ho3+ no LiYF4 (YLF) e no ZBLAN, para os íons desativadores Nd3+, Tb3+ ou Eu3+. Os microparâmetros de interação dessas TE foram obtidos utilizandose o método da integral de sobreposição e os resultados indicaram que o íon de Eu3+ é o melhor desativador do primeiro estado excitado do Ho3+ no YLF e o Nd3+ é o mais eficiente desativador do Er3+ no YLF e ZBLAN. A dependência temporal das fluorescências do Er3+ em 1,5 ; 2,7 m e do Ho3+ em 2,1 ; 2,9 m foram medidas utilizandose excitações laser pulsadas provenientes do Nd-YAG+2 +OPO sintonizável. Foi proposto um critério geral para a discriminação dos processos de TE assistidos pela migração da excitação entre doadores (difusão ou saltos). Verificou-se que o modelo de migração por difusão ajusta melhor os processos de TE do segundo estado excitado do doador (Er3+ or Ho3+) independentemente da razão CD-D / CD-A, enquanto que o modelo de migração por saltos aplica-se ao primeiro estado excitado do doador. Foi proposta uma modificação no modelo de saltos que descreve os resultados experimentais para sistemas com CD-D / CD-A> 10. Utilizando-se os parâmetros de TE verificamos que os melhores sistemas para a ação laser em 3µm são: Ho:Eu:YLF, Ho:Nd:YLF e Er:Nd:YLF. Por outro lado, verifica-se que os sistemas com baixas concentrações (1,5mol%) de Er:Nd; Er:Tb e Er:Eu no ZBLAN não apresentaram potencial de inversão de população para a ação laser em 2,8 m. Os processos de conversão ascendente no sistema Er:YLF foram estudados em função da concentração de Er3+, sendo que os processos de absorção de estado excitado (ESA) e de conversão ascendente por transferência de energia (ETU) foram discriminados utilizando as curvas de decaimento resolvidas no tempo. Observou-se que o comprimento de onda de excitação em 980nm é o mais adequado para o bombeamento do sistema Er:YLF para a emissão laser quase contínua (cw) em 2,8 m. A técnica de pump-probe foi utilizada a fim de serem investigados os efeitos nos tempos de vida do sistema Er:YLF, sendo verificada uma diminuição da contribuição da migração da excitação nos tempos de vida do primeiro e segundo estados excitados do Er3+ no YLF com o aumento da potência de bombeamento cw ( pump ). As taxas experimentais de TE, determinadas para os melhores sistemas por meio do parâmetro RN, foram utilizadas no sistema de equações de taxa e, resolvendo-as pelo método numérico de Runge-Kutta de 4a ordem, pudemos avaliar a densidade de população invertida para as emissões em 2,8 m do Er3+ e 2,9 m do Ho3+ em função das taxas de bombeamento e das concentrações dos íons ativador e desativador. A melhor concentração do sistema Er:YLF foi de 20mol% e no sistema Er:Nd:YLF foi de 4mol% de Er3+ e 1,5mol% de Nd3+. Verificou-se que o sistema Er(4mol%):Nd(1.5mol%):YLF favorece o aumento da freqüência máxima de operação de 14Hz no Er:YLF para 391Hz baseando-se na medida do tempo de vida do nível laser inferior (4I13/2) do Er3+. O sistema Ho3+ no YLF é otimizado utilizando-se 0,6mol% de Ho3+ e 1,5mol% de Nd3+ ou pelo sistema Ho(3mol%):Eu(1,2mol%):YLF, sendo que a densidade de população invertida observada no sistema Ho(3mol%):Eu(1,2mol%) é 2,4 vezes maior que no sistema Ho(0,6mol%):Nd(1,5mol%). / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP / FAPESP:00/11446-0

In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many different materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to finding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are provided with a mixture of numerical techniques, which suggest strong mathematical consistency within the model for all theoretical assumptions made. A physical experiment was undertaken and the results prove to be inaccurate when using parameters derived from tensile tests, but when back calculating parameters from the beam test the model has a 14.40% error at its extreme against the experimental data suggesting the necessity for further testing.

Les travaux exposés dans cette thèse sont consacrés à l’étude de méthodesprécises pour approcher des équations différentielles stochastiques ou deséquations aux dérivées partielles (EDP) déterministes. La première parties’inscrit dans le cadre du développement de méthodes visant à corriger le biaisdans les processus de diffusion paramétrique. Trois modèles sont étudiés enparticulier : Ornstein-Uhlenbeck, Auto-régressif et Moyenne mobile. A l’issuede ce travail, plusieurs approximations de biais ont été proposées suivant deuxapproches : la première consiste en un développement de Taylor del’estimateur obtenu alors que la seconde s'appuie sur une expansionstochastique de celui-ci.La deuxième partie de cette thèse porte sur l’approximation de l’équation de lachaleur obtenue après changement de variables à partir du modèle de Black etScholes. En général, on préfère utiliser des méthodes implicites pour résoudredes EDP paraboliques mais depuis quelques années, les méthodes dites deRunge-Kutta explicites stabilisées, sont de plus en plus utilisées. Nousmontrons que l’utilisation de ce type de méthodes explicites et notamment lesschémas ROCK donnent de très bons résultats même si les conditions initialessont peu régulières, ce qui est le cas dans les modèles financiers / The work presented in this thesis is devoted to the study of precise methods forapproximating stochastic differential equations (SDE) or deterministic partialdifferential equations (PDE). The first part is devoted to the development ofbias correction methods in parametric diffusion processes. Three models arestudied in particular : Ornstein-Uhlenbeck, auto-regressive and Movingaverage. At the end of this work, several approximations of bias have beenproposed following two approaches : the first consists in a Taylor developmentof the obtained estimator while the second one relies on a stochastic expansionof the latter.The second part of this thesis deals with the approximation of the heatequation obtained after changing variables from the Black-Scholes model. Likethe vast majority of PDE, this equation does not have an exact solution, sosolutions must be approached using explicit or implicit time schemes. Itis often customary to prefer the use of implicit methods to solve parabolic PDEsuch as the heat equation, but in the past few years, the stabilized explicitRunge-Kutta methods which have the largest possible domains of stabilityalong the negative real axis, are increasingly used. We show that the useof this type of explicit methods and in particular the ROCK (Runge-Orthogonal-Chebyshev-Kutta) schemes give very good results even if the initial conditionsare not very regular, which is the case in the financial models

Thesis is dedicated to evaluation of roundoff impact on numerical integration methods accuracy and effectivity. Contains theoretical expectations taken from existing literature, implementation of chosen methods, experimental measurement of attained accuracy under different circumstances and their comparison with regard to time complexity. Library contains Runge-Kutta methods to order 7 and Adams-Bashforth methods to order 20 implemented using C++ templates which allow optional arbitrary-precision arithmetic. Small models with known analytic solution were used for experiments.

No description available.

<p>This study focuses on developing a new online recursive numerical algorithm for a coupled nonlinear inverse heat conduction-microstructure problem. This algorithm is essential in identifying, designing and controlling many industrial applications such as the quenching process for heat treating of materials, chemical vapor deposition and industrial baking. In order to develop the above algorithm, a systematic four stage research plan has been conducted. </P> <p> The first and second stages were devoted to thoroughly reviewing the existing inverse heat conduction techniques. Unlike most inverse heat conduction solution methods that are batch form techniques, the online input estimation algorithm can be used for controlling the process in real time. Therefore, in the first stage, the effect of different parameters of the online input estimation algorithm on the estimate bias has been investigated. These parameters are the stabilizing parameter, the measurement errors standard deviation, the temporal step size, the spatial step size, the location of the thermocouple as well as the initial assumption of the state error covariance and error covariance of the input estimate. Furthermore, three different discretization schemes; namely: explicit, implicit and Crank-Nicholson have been employed in the input estimation algorithm to evaluate their effect on the algorithm performance. </p> <p> The effect of changing the stabilizing parameter has been investigated using three different forms of boundary conditions covering most practical boundary heat flux conditions. These cases are: square, triangular and mixed function heat fluxes. The most important finding of this investigation is that a robust range of the stabilizing parameter has been found which achieves the desired trade-off between the filter tracking ability and its sensitivity to measurement errors. For the three considered cases, it has been found that there is a common optimal value of the stabilizing parameter at which the estimate bias is minimal. This finding is important for practical applications since this parameter is usually unknown. Therefore, this study provides a needed guidance for assuming this parameter. </p> <p> In stage three of this study, a new, more efficient direct numerical algorithm has been developed to predict the thermal and microstructure fields during quenching of steel rods. The present algorithm solves the full nonlinear heat conduction equation using a central finite-difference scheme coupled with a fourth-order Runge-Kutta nonlinear solver. Numerical results obtained using the present algorithm have been validated using experimental data and numerical results available in the literature. In addition to its accurate predictions, the present algorithm does not require iterations; hence, it is computationally more efficient than previous numerical algorithms. </p> <p> The work performed in stage four of this research focused on developing and applying an inverse algorithm to estimate the surface temperatures and surface heat flux of a steel cylinder during the quenching process. The conventional online input estimation algorithm has been modified and used for the first time to handle this coupled nonlinear problem. The nonlinearity of the problem has been treated explicitly which resulted in a non-iterative algorithm suitable for real-time control of the quenching process. The obtained results have been validated using experimental data and numerical results obtained by solving the direct problem using the direct solver developed in stage three of this work. These results showed that the algorithm is efficiently reconstructing the shape of the convective surface heat flux. </P> / Thesis / Doctor of Philosophy (PhD)

This thesis deals with the creation of the intro with limited size. This work describes methods for reducing the size of the final application. The main part describes methods for generating graphic content and methods for its animation. It deals with creation of textures and geometry. Another part is aimed on the physical simulation of particle and elastic systems.

L'algorithme covariant de van Holten, servant à construire des quantités conservées, est présenté avec une attention particulière portée sur les vecteurs de type Runge-Lenz. La dynamique classique des particules portant des charges isospins est passée en revue. Plusieures applications physiques sont considerées. Des champs de type monopôles non-Abéliens, générés par des mouvements nucléaires dans les molécules diatomiques, introduites par Moody, Shapere et Wilczek, sont étudiées. Dans le cas des espaces courbes, le formalisme de van Holten permet de décrire la symétrie dynamique des monopôles Kaluza-Klein généralisés. La procédure est étendue à la supersymétrie et appliquée aux monopôles supersymétriques. Une autre application, concernant l'oscillateur non-commutatif en dimension trois, est également traitée.