The paper describes a storage scheme for sparse symmetric or nonsymmetric matrices which has been developed and used for many years at the Technical University of Chemnitz. An overview of existing library subroutines using such matrices is included.

In this paper, we investigate the question of the spectrally equivalence of the so- called Pseudo-Laplacian to the usual discrete Laplacian in order to use hierarchical preconditioners for this more complicate matrix. The spectral equivalence is shown to be equivalent to a Brezzi-type inequality, which is fulfilled for the finite element spaces considered here.

In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).

[pt] Neste trabalho é apresentada a formulação do modelo matemático de um elemento com número reduzido de graus-de-liberdade para a análise linear tridimensional de vigas. O elemento possui quatro graus-de-liberdade por ponto nodal, sendo três deslocamentos e uma rotação local da seção reta do elemento em relação ao eixo longitudinal da viga. Os efeitos de rotação local da seção reta do elemento em relação ao eixo longitudinal da viga. Os efeitos de rotação reta devido à flexão são considerados na formulação através da condição de não haver deformações transversais por cisalhamento. As condições de contorno de engastamento e de compatiblidade entre elementos contíguos são garantidas através de um procedimento de penalidade, introduzindo modificações no funiconal da energia potencial total da estrutura, assegurando a compatibilidade entre os elementos. Análises de algumas estruturas simples são apresentadas para demonstrar a eficiência da formulação, e suas soluções comparadas com resultados analíticos ou numéricos. A formulação é proposta de forma a ser facilmente estendida a análises mais gerais que incluam efeitos dinâmicos e de não linearidade do material. / [en] Throughout this thesis the formulation of the mathematical modelo f a general tri-dimensional beam element with reduced degrees-of-freedom is presented. The element is a four node displacement based finite element with three linear and one locally referrer rotational displacements at each node. Bending effects are taken into account through the imposition of non-transversal shear condition. Coupling between adjoining elements anda t the element clamped restraint is asssured by a penalty procedure imposed at the common node location. The analysis of some simple structures are presented and the solutions compared with other analytical or numerical results. The formulation hás been proposed so that it can be generally extended to material non-linear and dynamic analysis.

This thesis investigates violent air-water flows in two and three dimensions using a smoothed particle hydrodynamics (SPH) model accelerated using the parallel architecture of graphics processing units (GPUs). SPH is a meshless Lagrangian technique for CFD simulations, whose major advantage for multi-phase flows is that the highly nonlinear behaviour of the motion of the interface can be implicitly captured with a sharp interface. However, prior to this thesis performing multi-phase simulations of large scale air-water flows has been prohibitive due to the inherent high computational cost. The open source code DualSPHysics, a hybrid central processing unit (CPU) and GPU code, is heavily modified in order to be able to handle flows with multiple fluids by implementing a weakly compressible multi-phase model that is simple to implement on GPUs. The computational runtime shows a clear improvement over a conventional serial code for both two- and three dimensional cases enabling simulations with millions of particles. An investigation into different GPU algorithms focuses on optimising the multi-phase SPH implementation for the first time, leading to speedups of up to two orders of magnitude compared to a CPU-only simulation. Detailed comparison of different GPU algorithms reveals a further 12% improvement on the computational runtime. Enabling the modelling of cases with millions of fluid particles demonstrates some previously unreported problems regarding the simulation of the air phase. A new particle shifting algorithm has been proposed for multi-phase flows enabling the air, initially simulated as a highly compressible liquid, to expand rapidly as a gas and prevent the formation of unphysical voids. The new shifting algorithm is validated using dam break flows over a dry bed where good agreement is obtained with experimental data and reference solutions published in the literature. An improvement over a corresponding single-phase SPH simulation is also shown. Results for dam break flows over a wet bed are shown for different resolutions performing simulations that were unfeasible prior to the GPU multi-phase SPH code. Good agreement with the experimental results and a clear improvement over the single-phase model are obtained with the higher resolution showing closer agreement with the experimental results. Sloshing inside a rolling tank was also examined and was found to be heavily dependent on the viscosity model and the speed of sound of the phases. A sensitivity analysis was performed for a range of different values comparing the results to experimental data with the emphasis on the pressure impact on the wall. Finally, a 3-D gravity-driven flow where water is impacting an obstacle was studied comparing results with published experimental data. The height of the water at different points in the domain and the pressure on the side of the obstacle are compared to a state-of-the-art single-phase GPU SPH simulation. The results obtained were generally in good agreement with the experiment with closer results obtained for higher resolutions and showing an improvement on the single-phase model.

Orientador: Alexandre Campane Vidal / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Geociências / Made available in DSpace on 2018-08-24T10:58:04Z (GMT). No. of bitstreams: 1 Costanzo_CaetanoPontes_M.pdf: 3384236 bytes, checksum: 7b4516eef162c87ff3e03f0d56f08215 (MD5) Previous issue date: 2014 / Resumo: Em face da crescente demanda de execução de projetos de remediação de aquíferos contaminados, a técnica de bombeamento e tratamento está sendo utilizada de forma significativa. Esta ferramenta de recuperação ambiental consiste no bombeamento da água subterrânea em pontos estrategicamente posicionados de maneira a gerar uma barreira hidráulica que impeça o avanço da extensão de uma pluma de contaminação. Em áreas com alta heterogeneidade litológica, a organização espacial dos valores de condutividade hidráulica (K) em subsuperfície apresenta incertezas associadas à variabilidade na distribuição das fácies. No presente estudo foram analisadas estas incertezas por meio de métodos geoestatísticos (krigagem da indicatriz e simulações estocásticas) e também a partir de simulações numéricas de fluxo e transporte de contaminantes. Estas ferramentas permitiram a análise das possibilidades de deslocamentos espaciais das plumas de contaminação, bem como possíveis cenários de bombeamento e tratamento numa área contaminada, em função de distintos campos aleatórios de condutividade locais, devido à complexidade geológica. A partir da krigagem da indicatriz foi possível elaborar um modelo geoestatístico de fácies que foi utilizado como ferramenta para validar o uso da condutividade hidráulica em função de cada litologia, definindo assim os possíveis grupos de hidrofácies presentes na área. Por meio das simulações estocásticas foram gerados vinte campos distintos de condutividade hidráulica, os quais configuraram distintas distribuições espaciais das áreas das plumas de contaminação, como também cenários otimista, intermediário e pessimista para o deslocamento das mesmas. Foram simulados três cenários de bombeamento e tratamento resultando nove situações desta técnica de remediação. Dessa forma, os efeitos da heterogeneidade atrelada à condutividade hidráulica evidenciaram que, para a execução de um projeto de remediação por bombeamento e tratamento em áreas com certa heterogeneidade geológica, é necessária a análise de incertezas atreladas ao diagnostico hidrogeológico. Ao considerar modelos com homogeneidade na condutividade e mais simplistas, o projeto de remediação pode vir a ser ineficiente aumentando o tempo para a recuperação ambiental local e consequentemente aumentando os custos / Abstract: Due to the growing demand for project execution remediation of contaminated aquifers, the pump-and-treat is being used significantly. This remediation technique consists in groundwater pumping in strategically placed at points to generate a hydraulic barrier to prevent the advance of a contamination plume. In areas with high lithological heterogeneity, the spatial organization of the hydraulic conductivity (K) values in the subsurface introduces uncertainties associated with the variability in the distribution of facies. In this study these uncertainties were evaluated using geostatistical methods (indicator kriging and stochastic simulations) and also from numerical simulations of flow and contaminant transport. These tools enable the analysis of the contamination plumes areas, as well as scenarios for pump-and-treat, due to different random fields of local conductivity according to the geological complexity. By indicator kriging, was possible to provide a geostatistical facies model which was used as a tool to validate the hydraulic conductivity as a function of each lithology, thus defining the possible hydrofacies groups in the area. The stochastic simulations generated twenty distinct hydraulic conductivity fields, which represented different spatial distributions of contamination plumes, as well as scenarios optimistic, intermediate and pessimistic to offset these. Three scenarios for pump-and-treat were simulated resulting nine situations of this remediation technique. Therefore the effects of heterogeneity associated with hydraulic conductivity showed that, for the remediation design in areas with certain geological heterogeneity, the analysis of uncertainties linked to hydrogeological studies is needed. When considering models with homogeneous conductivity and most simplistic, the remediation project may prove to be inefficient increasing the time to the project and consequently increasing costs / Mestrado / Geologia e Recursos Naturais / Mestre em Geociências

Ces travaux s’inscrivent dans le cadre du projet ANR "CAPTIF" (CAPTeurs innovants Intégrés et logiciels au coeur d’un dispositif d’électronique de puissance). Ce projet s’intéresse aux solutions de suivi de vieillissement en temps réel de modules d’électronique de puissance pour réduire les coûts de maintenance et augmenter la fiabilité des systèmes de conversion d’énergie.Les limitations des modèles de fiabilité actuels sont mises en évidence et conduisent à la recherche d’une approche plus représentative des mécanismes entraînant la défaillance des modules de puissance et à une remise en question du traditionnel nombre de cycles moyens avant défaillance en tant qu’outil de gestion de la fiabilité. À partir de l’identification des mécanismes de vieillissement des assemblages de puissance, une nouvelle méthodologie de modélisation est proposée pour caractériser la durée de vie résiduelle d’un module, en s’appuyant sur un indicateur d’endommagement énergétique. La fonction de corrélation entre cet indicateur de vieillissement et les données issues de capteurs embarqués est alors construite à l’aide de méthodes de régression numérique. Une mise en application sur un assemblage représentatif illustre l’intérêt de la méthodologie. / This work is part of the french Research National Agency project called "CAPTIF" (meaning"Innovative embedded sensors and software for power electronics devices"). This research project deals with power electronics health monitoring solutions in order to increase electric conversion devices reliability and decrease maintenance costs.Traditionnal reliability models limitations led to a reconsideration of life prediction methodsand mean time to failure as a reliability management tool for power electronics devices.An investigation to develop an approach more representative of failure mechanisms observed in power electronics devices was conducted. Based on ageing mechanisms of power electronics assemblies, an ageing indicator was proposed and used with a modelling methodology to characterise the residual life of a device exposed to thermal loads. The functional link between this ageing indicator and data provided by embedded sensors is approache dusing a numerical design of experiment and a response surface methodology. This modelling process is illustrated by an application to a simplified power assembly.

O tema deste trabalho é o estudo de métodos numéricos para a simulação de escoamentos incompressíveis com superfície livre a baixos Reynolds, por meio da metodologia GENSMAC e suas formulações explícita e implícita. Neste contexto, temos especial interesse na formulação implícita, objetivando o enfraquecimento da restrição de estabilidade parabólica no passo temporal em escoamentos com superfície livre. O trabalho pode ser dividido em duas partes: na primeira, algumas modificações são discutidas, propostas e testadas com o objetivo de tornar a formulação implícita mais eficiente e precisa; em seguida, aproveitamos os resultados obtidos e generalizamos o método numérico existente para simular escoamentos viscoelásticos modelados pela equação constitutiva SXPP. Em ambos os casos, a formulação explícita também é usada para comparação e teste. Resultados que demonstram a eficiência e robustez das técnicas desenvolvidas são apresentados por meio da simulação numérica de complexos problemas envolvendo superfície livre.O tema deste trabalho é o estudo de métodos numéricos para a simulação de escoamentos incom- pressíveis com superfície livre a baixos Reynolds, por meio da metodologia GENSMAC e suas formulações explícita e implícita. Neste contexto, temos especial interesse na formulação implícita, objetivando o en- fraquecimento da restrição de estabilidade parabólica no passo temporal em escoamentos com superfície livre. O trabalho pode ser dividido em duas partes: na primeira, algumas modificações são discutidas, propostas e testadas com o objetivo de tornar a formulação implícita mais eficiente e precisa; em seguida, aproveitamos os resultados obtidos e generalizamos o método numérico existente para simular escoamentos viscoelásticos modelados pela equação constitutiva SXPP. Em ambos os casos, a formulação explícita também é usada para comparação e teste. Resultados que demonstram a eficiência e robustez das técnicas desenvolvidas são apresentados por meio da simulação numérica de complexos problemas envolvendo superfície livre / The purpose of this work is the study of numerical methods for low Reynolds number incompressible free surface flows, including the GENSMAC methodology and its explicit and implicit formulations. In this context, we have special interest in the implicit formulation, in order to circumvent the parabolic stability restriction in the time step for free surface flows. The work can be divided into two parts: firstly, some modifications are proposed, discussed, and tested with the purpose of making the implicit formulation more e¢ cient and accurate; secondly, we take advantage of the results derived in the first part to generalize the numerical method for simulating viscoelastic free surface flows modeled by the constitutive equation SXPP. In both cases, the explicit formulation is also used for comparison and tests. Results that demonstrate the e¢ ciency and robustness of the developed techniques are presented and illustrated by the numerical simulation of complex problems involving free surface flows

White dwarf stars are the most common final stage of stellar evolution, corresponding to 99% of all stars in the Galaxy. White dwarf models can be used to obtain the age of stellar populations, to build an initial to final mass relation to understand the connection between the properties of white dwarfs and their progenitors, determine the upper mass limit that separates white dwarfs progenitors from Type II supernovae, enhance the comprehension of the physical properties of high density matter and derive ages and masses for observed white dwarfs from the cooling tracks. The literature is populated with low mass and intermediate mass white dwarf models, however the massive white dwarfs are often forgotten and the evolutionary sequences are incomplete. In this dissertation, we compute full evolutionary sequences for massive white dwarfs, exploring the evolution of hydrogen-rich and hydrogen-deficient white dwarfs stars with masses between 1.012 and 1.307 M , and initial metallicity of Z = 0.02. These sequences are the result of main sequence stars with masses between 8.8 and 11.8 M . The simulations were performed with the Modules for Experiments in Stellar Astrophysics - MESA code, starting at the zero-age main sequence, through thermally pulsing and mass-loss phases, ending as the white dwarfs at the cooling sequence. Our simulations are full evolutionary, in which we consider the entire evolutionary history of the progenitors. We present reliable nuclear chemical profiles for the whole mass range considered, covering the different expected central compositions, i.e. C/O, O/Ne and Ne/O/Mg, and their dependence with the stellar mass. In addition, we present detailed chemical profiles of hybrid C/O-O/Ne core white dwarfs, found in the mass range between 1.024 and 1.150 M . We present the initial-to-final mass relation, mass-radius relation, and cooling times with improved crystallization limits, considering the effects of atmosphere and core composition.

In this thesis, we compute approximate solutions to initial value problems of first-order linear ODEs using five explicit Runge-Kutta methods, namely the forward Euler method, Heun's method, RK4, RK5, and RK8. This thesis aims to compare the accuracy, stability, and efficiency properties of the five explicit Runge-Kutta methods. For accuracy, we carry out a convergence study to verify the convergence rate of the five explicit Runge-Kutta methods for solving a first-order linear ODE. For stability, we analyze the stability of the five explicit Runge-Kutta methods for solving a linear test equation. For efficiency, we carry out an efficiency study to compare the efficiency of the five explicit Runge-Kutta methods for solving a system of first-order linear ODEs, which is the main focus of this thesis. This system of first-order linear ODEs is a semi-discretization of a two-dimensional wave equation.