Made available in DSpace on 2015-05-15T11:46:10Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 705090 bytes, checksum: 6259c1312a92c4f8f051446d8ad30afc (MD5) Previous issue date: 2012-04-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we obtain existence, nonexistence and multiplicity of solutions for the elliptic partial differential equation u 1 2 (x:ru) + "jujp1u = u; x 2 RN; where N 3, " = 1, > 0 and 1 < p (N + 2)=(N 2). Such equation is obtained when we look for self-similar solutions for certain nonlinear heat equations. To obtain the main results, we use variational methods, more precisely, minimization arguments, Lagrange multipliers theorem and elliptic regularity results. / Neste trabalho, obtemos resultados de existência, não existência e multiplicidade de soluções para a equação diferencial parcial elíptica u 1/2(x:ru) + "jujp1u = u; x 2 RN; em que N 3, " =1, > 0 e 1 < p (N + 2)=(N 2). Tal equação é obtida quando procuramos soluções autossimilares para certas equações do calor não-lineares. Para a obtenção dos resultados principais, usamos métodos variacionais, mais precisamente, argumentos de minimização, Teorema dos Multiplicadores de Lagrange e resultados de regularidade elíptica.

Made available in DSpace on 2015-05-15T11:46:18Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1803826 bytes, checksum: 7e6b888ce249e6a65e6ceb39484c36e5 (MD5) Previous issue date: 2010-08-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In the present work, we study controllability results for two problems on the theory of the partial differential equations. We use global Carleman inequalities to show the null controllability for the heat equation and for a PDE with complex principal part. We obtain the control of minimal norm solving a dual minimization problem. / No presente trabalho, estudaremos resultados de controlabilidade para dois problemas da teoria das equações diferenciais parciais. Por meio de estimativas globais de Carleman, mostraremos detalhadamente a controlabilidade nula para a equação do calor e para uma equação diferencial parcial com parte principal complexa. Obteremos o controle de norma mínima resolvendo um problema dual de minimização.

Orientador: Igor Leite Freire / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T07:51:21Z (GMT). No. of bitstreams: 1 Soares_JuniorCesarAlves_M.pdf: 448504 bytes, checksum: 3bdbb23b41bf8a05b373b9117cd9aa9b (MD5) Previous issue date: 2011 / Resumo: Neste trabalho, é estudada uma generalização da equação de Burgers do ponto de vista da teoria de simetrias de Lie / Abstract: In this work, a generalization of Burgers equation is studied from the point of view of Lie point symmetry theory / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

We employ two efficient parallel approaches to reduce a model arising from a semi-discretization of a controlled heat transfer process for optimal cooling of a steel profile. Both algorithms are based on balanced truncation but differ in the numerical method that is used to solve two dual generalized Lyapunov equations, which is the major computational task. Experimental results on a cluster of Intel Xeon processors compare the efficacy of the parallel model reduction algorithms.

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The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear problems (convection, heat conduction) and also for nonlinear problems (Burgers' and KdV equations) were performed. The compact solvers were combined with Euler and fourth-order Runge-Kutta time differencing. In most cases, the order of convergence of the numerical solution to the exact solution was the same as the formal order of accuracy of the compact schemes employed.

For the future implementation of high speed communication,safety remains one of the main concerns. To ensurethe safety of new applications, specifically the new 5G antennas,it is crucial to know that they will not cause any harm to thehuman body. There are a few ways to test how safe a systemusing high frequency radiation is but the industry standard is byusing the Specific Absorption Rate (SAR). The SAR is directlycorrelated to the initial temperature rise in the volume exposedto radiation which is what the method used in this report is basedon. The temperature rise in a skin-like phantom due to 5 GHzexposure was recorded using an IR-camera, which in turn wasused to calculate the SAR. The purpose of this report was to testif this method is a valid way of obtaining the peak surface SAR.It was concluded that the method is valid but there are someuncertainties in regards to abstracting the method to far-fieldexposure for our considered frequency. The SAR value that isachieved in this report is 333.4 W/Kg which is high in relationto the SAR-limits in IEEE guidelines, although the set up is notsupposed to reflect a realistic use of the antenna. This is due tothe fact that the waveguide in the setup is close to measurementsample, and has a higher intensity than is to be expected fromreal world applications. The method may be applicable for farfieldexposure with a higher frequency as that would concentratethe measurable heat to the surface of the measurement sampleand would also carry more energy by default. / För all framtida implementering avhöghastighetskommunikation kommer säkerhetsgarantin varaen av de stora frågorna. För att fastställa säkerheten hos nyatillämpningar, specifikt 5G antenner, är det viktigt att vetaatt det är oskadligt för människor. Det finns olika metoderför att påvisa säkerheten i applikationer som använder sig avhögfrekvent strålning men industristandarden är att användaSAR (Specific Absorption Rate). SAR är direkt korrelerat medvärmeutvecklingen i volymen utsatt för strålning vilket är detfaktum denna rapport är baserad på. Temperaturökningeni en skinnliknande fantom från 5 GHz-strålning mättes meden IR-kamera. Detta användes för att räkna ut SAR-värdet.Poängen med rapporten var att testa om denna metod äracceptabel för att räkna ut högsta SAR-värdet i en punkt.Slutsatsen är att denna metod fungerar men det kan finnasproblem med att abstrahera metoden till fjärrfält för vårtilltänka frekvens. Det uppnådda SAR-värdet är 333.4 W/Kgvilket är högt jämfört med IEEE-standarden, detta är på grundav att uppställningen inte är tänkt att återspegla en realistisksituation. Antennen är för nära fantomen och intensiteten ärockså högre än vad som används i vanliga fall. Metoden kanmöjligtvis användas vid fjärrfältstrålning vid högre frekvenseri och med att detta leder till en värmeökning koncentrad vidytan. Dessutom har högre frekvenser högre energi vilket innebären större värmeökning. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

Submitted by Maria Cristina (library@lncc.br) on 2017-08-15T11:59:17Z No. of bitstreams: 1 Dissertação_Daiana.pdf: 879097 bytes, checksum: a1ed3aca0b5dd3e6a29a655e3fdb4aff (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2017-08-15T11:59:28Z (GMT) No. of bitstreams: 1 Dissertação_Daiana.pdf: 879097 bytes, checksum: a1ed3aca0b5dd3e6a29a655e3fdb4aff (MD5) / Made available in DSpace on 2017-08-15T11:59:38Z (GMT). No. of bitstreams: 1 Dissertação_Daiana.pdf: 879097 bytes, checksum: a1ed3aca0b5dd3e6a29a655e3fdb4aff (MD5) Previous issue date: 2017-06-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes) / In this work, numerical analysis is developed for a hybrid stabilized finite element method for transient heat conduction problems. Classically, numerical solutions for these problems are commonly obtained by the use of the standard Galerkin method. However, when used with small time steps and fixed meshes, spurious oscillations arise as time increases, disturbing the solution at the initial time steps. By contrast, the approach used here to solve those problems consists in the application of a hybrid stabilized finite element method for spatial approximations combined with finite difference methods, more specifically Euler and Crank-Nicolson techniques, for the temporal approach. The utilized hybrid method is based on the Discontinuous Galerkin method (DG) and is constructed through the coupling of local problems, from which the solution of the primal variable is obtained, with a global problem associated to the Lagrange multiplier degrees of freedom identified with the trace of the primal variable; continuity between elements being imposed weakly. The numerical analysis shows that the proposed formulation retains the main characteristics of the associated DG methods such as consistency, stability, continuity and optimal orders of convergence in the energy norm. Numerical experiments are presented confirming the developed theoretical analysis and showing the lack of spurious oscillations in small times. / Neste trabalho, uma análise numérica é desenvolvida para um método híbrido estabilizado de elementos finitos para problemas transientes de condução de calor. Classicamente, soluções numéricas para esses problemas são comumente encontradas utilizando-se o básico método de Galerkin. Contudo, quando utilizado com passos de tempo reduzidos e malhas de tamanho fixo, oscilações espúrias espaciais aparecem à medida que o tempo aumenta, poluindo a solução nos tempos iniciais. Em contrapartida, a abordagem aqui empregada para obter a solução desses problemas consiste na aplicação de um método de elementos finitos híbrido estabilizado para a aproximação espacial, combinado com esquemas de diferenças finitas, mais precisamente os métodos de Euler e de Crank-Nicolson, para a aproximação temporal. O método híbrido utilizado é baseado no método de Galerkin Descontínuo (GD) e construído através do acoplamento de problemas locais, de onde a solução da variável primal é encontrada, com um problema global que está associado aos graus de liberdade do multiplicador de Lagrange identificado ao traço da variável primal; sendo a continuidade entre os elementos imposta de forma fraca. A análise numérica mostra que a formulação proposta preserva as principais características dos métodos GD associados, tais como consistência, estabilidade, continuidade e taxas ótimas de convergência na norma da energia. Experimentos numéricos são apresentados confirmando as análises teóricas aqui desenvolvidas e evidenciando a ausência de oscilações espúrias para pequenos tempos.

Ce travail de thèse a pour but d'étudier des écoulements non stationnaires de fluides incompressibles Newtoniens et non isothermes. Le problème est décrit par les lois de conservation de la masse, de la quantité de mouvement et de l'énergie. Nous nous intéressons au couplage entre le système de Navier-Stokes et l’équation de la chaleur hyperbolique (le résultat de la combinaison entre la loi de conservation d'énergie et la loi de Cattaneo). Cette dernière est une modification de la loi de Fourier utilisée habituellement, elle permet de surmonter « le paradoxe de la chaleur » et d'obtenir une description plus précise de la propagation de la chaleur. Le système couplé est un problème hyperbolique-parabolique dont la viscosité dépend de la température, alors que la capacité thermique et le terme de dissipation dépendent de la vitesse. Afin d’obtenir un résultat d'existence de solutions du problème couplé, nous démontrons d'abord l'existence et l'unicité de la solution du problème hyperbolique puis nous introduisons une discrétisation en temps et nous étudions la convergence des solutions approchées vers celles du problème original. Dans un deuxième temps nous étudions l'existence et l'unicité de la solution du système de Navier-Stokes muni des conditions aux limites de type Tresca puis de type Coulomb en dimension 2 et 3. Dans le chapitre 3, nous proposons une discrétisation en temps du problème d'écoulement dans le cas de la condition au limite de type Tresca et nous établissons la convergence des solutions approchées. Le dernier chapitre de ce mémoire est consacré à l'étude du problème couplé dans le cas de conditions aux limites de type Tresca. L'existence d'une solution est obtenue par un argument théorique de point fixe en dimension 2 et également par une méthode de discrétisation en temps qui conduit à résoudre sur chaque sous intervalle de temps un problème découplé pour la vitesse et la pression d'une part et la température d'autre part / The main objective of this thesis is to study nonstationary flows of incompressible Newtonian and non isothermal fluids. The problem is described by the laws of conservation of mass, momentum and energy. We consider the coupling between the Navier-Stokes system and the hyperbolic heat equation (the result of combination between the law of conservation of energy and the Cattaneo’s law). This one is a modification of the commonly used Fourier's law, it overcomes "the heat paradox" and gives a more accurate description of heat propagation. The coupled system is an hyperbolic-parabolic problem where the viscosity depends on the temperature but the thermal capacity and the dissipative term depend on the velocity. To obtain an existence result for the coupled system, we first prove the existence and uniqueness of the solution of the hyperbolic problem then we introduce a time discretization and we study the convergence of the approximate solutions to those of the original problem. In the second chapter, we study the existence and uniqueness of the solution of Navier-Stokes system with Tresca or Coulomb boundary conditions in dimension 2 and 3. In the third chapter, we propose a time discretization of the flow problem in the case of Tresca boundary conditions and we establish the convergence of the approximate solutions. The last chapter is devoted to the study of the coupled problem in the case of Tresca free boundary conditions. The existence of a solution is obtained by a theoretical argument (fixed-point theorem) in dimension 2 and also by a method of time discretization leading, on each time subinterval, to a decoupled problem for the velocity and pressure of a hand and the temperature of the other hand

On s'interesse aux problèmes elliptiques avec coéficients variables à travers des interfaces intérieures. La solution et ses dérivées normales peuvent subir des variations significatives à travers les frontières intérieures. On présente une méthode compacte aux différences finies sur des maillages adaptés de type octree conçues pour une résolution en parallèle. L'idée principale est de minimiser l'erreur de troncature sur la discretisation locale, en fonction de la configuration du maillage, en rapprochant une convergence à l'ordre deux. On montrera des cas 2D et 3D des résultat liés à des applications concrètes. / We consider problems governed by a linear elliptic equation with varying coéficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second order accuracy. Numerical illustrations relevant for actual applications are presented in two and three-dimensional configurations.