In this paper we develop new preconditioned iterative methods for solving monotone nonlinear eigenvalue problems. We investigate the convergence and derive grid-independent error estimates for these methods. Numerical experiments demonstrate the practical effectiveness of the proposed methods for a model problem.

Background Physics-based snow simulation in real time is an unexplored area, the reason being the difficulty introduced by the multitude of factors that affect the snow behaviour, such as cohesion, thermodynamics, and compression. Simulating snow in real time when considering these factors can become computationally demanding. However, the continued advancement of graphics processing units makes the exploration of real-time snow simulation attractive. Recently published research on real time physics-based snow simulation shows promising results in a parallel solution and will serve as motivation and base for this thesis. Objectives This thesis aims to improve the time-step of a previously proposed method using an iterative method and improve the snow behaviour with a particle-based boundary handling implementation. The aim consists of the following objectives. Integrate an iterative method, extend the snow behaviour with additional snow types, and implement a particle-based boundary handling method with two-way coupling. The proposed method should remain comparable to the original method in terms of snow behaviour. In order to gather results, the methods are measured in performance and used in a questionnaire to analyse the behaviour. Methods An iterative method along with a particle-based boundary handling method is implemented. The methods are both measured and compared using quantitative tests. Additionally, a questionnaire is deployed to gather qualitative results about the behaviour of the snow. Results The proposed method outperforms the original method in terms of time-step size. The proposed method is capable of increasing the time-step tenfold while decreasing the execution time by approximately eight times. Finally, the results from the questionnaire verify the perceived naturalism of the snow and its comparability to the original method. Conclusions The proposed method can perform with an increased time-step and a lower execution time compared to the original method, at the cost of time spent per frame. Lastly, the snow is perceived as natural with the boundary handling method at a significance level of 1 %. / Bakgrund Fysikbaserad snösimulering i realtid är ett outforskat område, anledning till detta är mängden faktorer som påverkar snö, exempelvis sammanhållning, termodynamik och kompression. Simulering av snö i realtid som tar hänsyn till dessa faktorer kan bli beräkningsmässigt krävande, däremot har den växande utvecklingen av grafikprocessorer gjort utforskning av realtidsmetoder ytterligare attraktivt. Nyligen publicerad forskning inom fysikbaserade snösimuleringar i realtid visar lovande resultat i en parallell lösning och kommer att användas som motivering samt bas i detta examensarbete. Syfte Detta examensarbete syftar till att förbättra tidsstegen i en tidigare implementerad metod med hjälp av att använda ett iterativt tillvägagångssätt samt förbättra snöbeteendet med en partikelbaserad gränshanteringsimplementation. Syftet är uppdelat i följande mål. Integrera en iterativ metod, utöka snöbeteendet med ytterligare snötyper, och implementera en partikelbaserad gränshanteringsmetod med tvåvägskoppling. Den föreslagna metoden ska förhålla sig jämförbar med originalmetoden med avseende på snöbeteendet. Slutligen för att samla in resultat mäts metoderna i prestanda och dessutom används ett frågeformulär för att analysera beteendet. Metod En iterativ metod tillsammans med en partikelbaserad gränshanteringsmetod är implementerad. Båda metoderna mäts och jämförs med hjälp av kvantitativa tester. Dessutom distribueras ett kvalitativt frågeformulär för att samla resultat om snöns beteende.  Resultat Den föreslagna metoden tillåter större tidsteg än originalmetoden. Den iterativa metoden är kapabel till att förstora tidsstegen tiofaldigt, samtidigt som den sänker exekveringstiden till en åttondel. Resultaten verifierar den uppfattade naturligheten av snön och jämförelsebarheten till originalmetoden. Slutsatser Den föreslagna metoden kan prestera med ett större tidssteg och en lägre exekveringstid jämfört med originalet i utbyte av högre tid spenderad per bildruta. Slutligen uppfattas snön som naturlig i sammankoppling med gränshanteringsmetoden vid en signifikansnivå på 1 %.

In recent years, techniques that had been developed for the combination of unification algorithms for equational theories were extended to combining constraint solvers. These techniques inherited an old deficit that was already present in the ombination of equational theories which makes them rather unsuitable for pratical use: The underlying combination algorithms are highly non-deterministic. This paper is concerned with the pratical problem of how to optimise the combination method of Baader and Schulz. We present two optimisation methods,called the iterative and the deductive method. The iterative method reorders and localises the non-deterministic decisions. The deductive method uses specific algorithms for the components to reach certain decisions deterministically. Run time tests of our implementation indicate that the optimised combination method yields combined decision procedures that are efficient enough to be used in practice.

No description available.

[pt] O objetivo deste trabalho é complementar a ferramenta de dimensionamento de pórticos planos de concreto armado já existente no Ftool, programa educacional amplamente difundido no meio acadêmico. Para tanto, foi introduzido o cálculo e dimensionamento de pilares de concreto armado à flexão composta reta. Foi adicionada uma nova seção transversal, referente aos pilares retangulares com armaduras simétricas. Além disso, foi necessária a inclusão de um método de análise não linear geométrica simplificado que fosse compatível com a filosofia do Ftool, aliando simplicidade e eficiência: o método dos Dois Ciclos Iterativos. A ferramenta para análise não linear geométrica pode ou não ser utilizada em conjunto com a ferramenta para o dimensionamento de estruturas de concreto armado, sendo possível a análise não linear geométrica de pórticos planos constituídos de outros materiais. A metodologia utilizada para o dimensionamento dos pilares em concreto armado é a que se baseia nas zonas de solicitação e foi adequada para estar de acordo com a norma brasileira vigente, a ABNT NBR 6118:2014, assim como o dimensionamento de vigas existente em uma versão anterior dessa ferramenta. Dessa forma, é possível exibir resultados para pórticos planos compostos por vigas e pilares em concreto armado, nos mesmos moldes da versão anterior, com diagramas para as armaduras longitudinal e transversal disponíveis nos modos necessária e adotada. / [en] The main objective of this work is to complement the reinforced concrete plane frames design tool already existing in Ftool, an educational tool widely known in academia. Therefore, the design of reinforced concrete columns was introduced. A new cross section for rectangular columns with symmetrical steel reinforcement was added. In addition to that, the inclusion of a simplified nonlinear geometric analysis that was in accordance to the philosophy of Ftool, combining simplicity and efficiency, was needed: the Two cycles iterative method. The nonlinear geometric analysis tool may or may not be used together with the reinforced concrete plane frames design tool, thus allowing for geometric nonlinear analyses of plane frames of other materials. The methodology used for the reinforced concrete frames design was based on solicitation zones and was adapted to be in accordance with the Brazilian code, the ABNT NBR 6118:2014, as was the existing reinforced concrete beams design tool. It is now possible to show results for plane frames composed of reinforced concrete columns and beams just as in the previous version of the reinforced concrete design tool, showing diagrams for the necessary and adopted longitudinal and transversal steel reinforcement.

Made available in DSpace on 2014-08-20T14:25:46Z (GMT). No. of bitstreams: 1 dissertacao_marieli_sallet.pdf: 231023 bytes, checksum: f445526b62fbfcde40fb1bc5ca90923a (MD5) Previous issue date: 2007-02-23 / Currently, the search for analytical solutions for the dispersion problems is one of the main research subjects in the pollutant dispersion modeling. These solutions become important due to the intention to obtain dispersion models that generate reliable results in a small computational time, which are of great interest for regulatory air quality applications. Lagrangian particle models are an important and effective tool to simulate the atmospheric dispersion of airborne pollutants. These models are based on the Langevin equation, which is derived from the hypothesis that the velocity is given by the combination between a deterministic term and a stochastic term. In this work is presented a new Lagrangian particle model to simulate the pollutant dispersion in low wind speed conditions. During low wind speed, the diffusion of a pollutant in the planetary boundary layer (PBL) is indefinite and it has been observed that the plume is subject to a great deal of horizontal undulations, which are called plume meandering. The method proposed leads to a stochastic integral equation whose solution has been obtained through the Method of Successive Approximations or Picard s Iteration Method. The integral equation is written in terms of the real and imaginary parts of the complex function before performing the multiplication of the integrating factor, expressed by the Euler formula, inside and outside of the integral solution. To take account the meandering effect, the Frenkiel s Eulerian autocorrelation functions for low wind conditions is included naturally in the model. The new approach has been evaluated through the comparison with experimental data and other different dispersion models. Particularly, the results obtained by the model agree very well with the experimental data, indicating the model represents the dispersion process correctly in low wind speed conditions. It is also possible to verify that the new model results are better than ones obtained by the other models. The analytical feature of the technique and the natural inclusion of the Frenkiel s Eulerian autocorrelation function become the model more accurate than other models. / Atualmente, a busca por soluções analíticas para os problemas de dispersão é um dos principais assuntos de pesquisa na modelagem da dispersão de poluentes. Estas soluções tornam-se importantes devido à intenção de obter modelos de dispersão que geram resultados confiáveis em um tempo computacional pequeno, que são de grande interesse para aplicações no controle da qualidade do ar. Modelos de partícula Lagrangeano são uma ferramenta importante e eficaz para simular a dispersão atmosférica de poluentes do ar. Esses modelos são baseados na equação de Langevin, que é derivada da hipótese que a velocidade é dada por uma combinação entre um termo determinístico e um termo estocástico. Neste trabalho é apresentado um novo modelo de partícula Lagrangeano para simular a dispersão de poluentes em condições de velocidade de vento fraco. Durante a velocidade de vento fraco, a difusão de um poluente na Camada Limite Planetária (CLP) é indefinida e tem sido observado que a pluma está sujeita a grandes ondulações horizontais, que são chamadas meandro do vento. O método proposto leva a uma equação integral estocástica cuja solução é obtida através do Método das Aproximações Sucessivas ou Método Iterativo de Picard. A equação integral é escrita em termos das partes real e imaginária da função complexa antes de realizar a multiplicação do fator integrante, expresso pela fórmula de Euler, dentro e fora da solução integral. Para considerar o efeito do meandro, as funções de autocorrelação Euleriana de Frenkiel para condições de vento fraco são incluídas naturalmente no modelo. A nova aproximação foi avaliada através da comparação com dados experimentais e outros diferentes modelos de dispersão. Particularmente, os resultados obtidos pelo modelo concordam muito bem com os dados experimentais, indicando que o modelo representa o processo de dispersão corretamente em condições de velocidade de vento fraco. Também é possível verificar que os resultados do novo modelo são melhores do que os obtidos pelos outros modelos. A característica analítica da técnica e a inclusão natural da função de autocorrelação Euleriana de Frenkiel tornam o modelo mais exato que os outros modelos.

Cette thèse traite d’une nouvelle classe de préconditionneurs qui ont pour but d’accélérer la résolution des grands systèmes creux, courant dans les problèmes scientifiques ou industriels, par les méthodes itératives préconditionnées. Pour appliquer ces préconditionneurs, la matrice d’entrée doit être réorganisée avec un algorithme de dissection emboîtée. Nous introduisons également une technique de recouvrement qui s’adapte à l’idée de chevauchement des sous-domaines provenant des méthodes de décomposition de domaine, aux méthodes de dissection emboîtée pour améliorer la convergence de nos préconditionneurs.Les résultats montrent que cette technique de recouvrement nous permet d’améliorer la vitesse de convergence de Nested SSOR (NSSOR) et Nested Modified incomplete LU with Rowsum proprety (NMILUR) qui sont des préconditionneurs que nous étudions. La dernière partie de cette thèse portera sur nos contributions dans le domaine du calcul parallèle. Nous présenterons la distribution des données et les algorithmes parallèles utilisés pour la mise en oeuvre de nos préconditionneurs. Les résultats montrent que sur une grille régulière 400x400x400, le nombre d’itérations nécessaire à la résolution avec un de nos préconditionneurs, Nested Filtering Factorization préconditionneur (NFF), n’augmente que légèrement quand le nombre de sous-domaines augmente jusqu’à 2048. En ce qui concerne les performances d’exécution sur le super-calculateur Curie, il passe à l’échelle jusqu’à 2048 coeurs et il est 2,6 fois plus rapide que le préconditionneur Schwarz Additif Restreint (RAS) qui est un des préconditionneurs basés sur les méthodes de décomposition de domaine implémentés dans la bibliothèque de calcul scientifique PETSc, bien connue de la communauté. / This thesis addresses a new class of preconditioners which aims at accelerating solving large sparse systems arising in scientific and engineering problem by using preconditioned iterative methods. To apply these preconditioners, the input matrix needs to be reordered with K-way nested dissection. We also introduce an overlapping technique that adapts the idea of overlapping subdomains from domain decomposition methods to nested dissection based methods to improve the convergence of these preconditioners. Results show that such overlapping technique improves the convergence rate of Nested SSOR (NSSOR) and Nested Modified Incomplete LU with Rowsum property (NMILUR) precondtioners that we worked on. We also present the data distribution and parallel algorithms for implementing these preconditioners. Results show that on a 400x400x400 regular grid, the number of iterations with Nested Filtering Factorization preconditioner (NFF) increases slightly while increasing the number of subdomains up to 2048. In terms of runtime performance on Curie supercomputer, it scales up to 2048 cores and it is 2.6 times faster than the domain decomposition preconditioner Restricted Additive Schwarz (RAS) as implemented in PETSc.

K nahrazení člověka při úloze testování dotykových embedded zařízení je zapotřebí vyvinout komplexní automatizovaný robotický systém. Jedním ze zásadních úkolů je tento systém automaticky zkalibrovat. V této práci jsem se zabýval možnými způsoby automatické kalibrace robotického ramene v prostoru ve vztahu k dotykovému zařízení pomocí jedné či více kamer. Následně jsem představil řešení založené na estimaci polohy jedné kamery pomocí iterativních metod jako např. Gauss-Newton nebo Levenberg-Marquardt. Na konci jsem zhodnotil dosaženou přesnost a navrhnul postup pro její zvýšení.

Due to their large torque-speed ratio and transmission efficiency, planetary gears are widely used in the automotive industry. However, high amplitude vibrations remain their critical weakness, which limits their usage especially when new strict noise legislations come into action. A new approach to handle the instability problems of planetary gears encountered in real industrial context is presented in this work. First, the dynamic response of a planetary gear failing to pass the noise regulations is theoretically investigated through an analytical model. The equations of motion were solved using the Spectral Iterative Method. The observed experimental results correlated well with those from the developed model. In order to limit the resonance phenomena, impacts of different macro and micro-geometry modifications were analytically investigated: quadratic teeth profile, different planets positioning, different number of teeth and number of planets. Optimum modifications were retrieved and are expected to be tested experimentally on a test bench and on the truck. Finally, the analytical model’s limits and sensitivity to different parameters were investigated in order to certify its reliability, and suggestions for improvements were presented.

A new vortex model for wind turbines was developed in order to evaluate the loads at the blades and other important characteristics of interest for the wind industry such as power and thrust coefficients. Nowadays, the calculation of these quantaties is done in a reliable and precise manner with LES simulation using actuator line or actuator disk models. However, LES simulations are computationally heavy and the model here developed aims at calculating the same quantities of interest in less time but still giving reliable and accurate results for any wind turbine model. The idea of a vortex model for wind turbines was developed by Segalini & Aöfredsson, J. Fluid Mech., vol. 725, pages 91-116, 2013, using vortex filaments to reproduce the vorticity on the blades and in the wake. Nevertheless, that model had some limitations, among which, the main one, was the impossibility to simluate wind turbines with varying circulation along the blade, something that is always present in reality. With this thesis it is proposed a model based on the one of Segalini & Alfredsson (2013) but with the introduction of a vortex sheet that allows to simulate a vorticity release from the wind turbine blades and hence wind turbines with varying circulation along the blades. The model was validated against a LES simulation of the Tjaereborg wind turbine by Sarmast, KTH Royal Institute of Technology, 2014, that utilized an actuator line model. The results confirmed the improvement of the vortex model compared to the previous one of Segalini & Alfredsson (2013) and gave consistent results regarding the flow field at the rotor plane and the loads on the blades.